LMFDB - Embedded newform 675.2.ba.b.257.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			257.4
Character	$\chi$	$=$	675.257
Dual form			675.2.ba.b.218.4

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23715 - 0.866263i) q^{2} +(-1.45553 - 0.938839i) q^{3} +(0.0960923 + 0.264011i) q^{4} +(0.987435 + 2.42236i) q^{6} +(-0.677826 - 1.45360i) q^{7} +(-0.671958 + 2.50778i) q^{8} +(1.23716 + 2.73303i) q^{9} +(-1.78545 - 2.12782i) q^{11} +(0.107999 - 0.474493i) q^{12} +(-0.176418 - 0.251952i) q^{13} +(-0.420628 + 2.38550i) q^{14} +(3.43416 - 2.88160i) q^{16} +(1.88139 + 7.02145i) q^{17} +(0.836964 - 4.45287i) q^{18} +(-5.07203 + 2.92834i) q^{19} +(-0.378100 + 2.75214i) q^{21} +(0.365624 + 4.17910i) q^{22} +(-0.116642 - 0.0543910i) q^{23} +(3.33246 - 3.01930i) q^{24} +0.464527i q^{26} +(0.765143 - 5.13951i) q^{27} +(0.318634 - 0.318634i) q^{28} +(1.51659 + 8.60103i) q^{29} +(4.22026 - 1.53605i) q^{31} +(-1.57207 + 0.137538i) q^{32} +(0.601106 + 4.77337i) q^{33} +(3.75485 - 10.3164i) q^{34} +(-0.602668 + 0.589247i) q^{36} +(-2.08386 + 0.558369i) q^{37} +(8.81158 + 0.770913i) q^{38} +(0.0202409 + 0.532353i) q^{39} +(-4.62442 - 0.815410i) q^{41} +(2.85184 - 3.07728i) q^{42} +(0.429127 - 4.90494i) q^{43} +(0.390200 - 0.675847i) q^{44} +(0.0971868 + 0.168333i) q^{46} +(7.69135 - 3.58654i) q^{47} +(-7.70389 + 0.970146i) q^{48} +(2.84600 - 3.39173i) q^{49} +(3.85358 - 11.9863i) q^{51} +(0.0495656 - 0.0707870i) q^{52} +(-0.483003 - 0.483003i) q^{53} +(-5.39876 + 5.69554i) q^{54} +(4.10079 - 0.723079i) q^{56} +(10.1318 + 0.499526i) q^{57} +(5.57450 - 11.9546i) q^{58} +(7.43127 + 6.23558i) q^{59} +(2.50049 + 0.910105i) q^{61} +(-6.55173 - 1.75553i) q^{62} +(3.13415 - 3.65086i) q^{63} +(-5.70071 - 3.29131i) q^{64} +(3.39133 - 6.42609i) q^{66} +(0.884390 - 0.619257i) q^{67} +(-1.67295 + 1.17142i) q^{68} +(0.118712 + 0.188676i) q^{69} +(9.03942 + 5.21891i) q^{71} +(-7.68515 + 1.26605i) q^{72} +(6.65047 + 1.78199i) q^{73} +(3.06175 + 1.11439i) q^{74} +(-1.26050 - 1.05768i) q^{76} +(-1.88278 + 4.03763i) q^{77} +(0.436116 - 0.676135i) q^{78} +(2.04188 - 0.360038i) q^{79} +(-5.93887 + 6.76239i) q^{81} +(5.01475 + 5.01475i) q^{82} +(-7.55956 + 10.7962i) q^{83} +(-0.762929 + 0.164636i) q^{84} +(-4.77986 + 5.69642i) q^{86} +(5.86754 - 13.9429i) q^{87} +(6.53585 - 3.04772i) q^{88} +(-5.58181 - 9.66798i) q^{89} +(-0.246656 + 0.427222i) q^{91} +(0.00315146 - 0.0360214i) q^{92} +(-7.58484 - 1.72638i) q^{93} +(-12.6222 - 2.22564i) q^{94} +(2.41732 + 1.27573i) q^{96} +(11.8062 + 1.03291i) q^{97} +(-6.45906 + 1.73070i) q^{98} +(3.60649 - 7.51214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.23715	−	0.866263i	−0.874798	−	0.612540i	0.0475633	−	0.998868i	$-0.484854\pi$
$2$	−1.23715	−	0.866263i	−0.874798	−	0.612540i	−0.922361	+	0.386328i	$0.873743\pi$
$3$	−1.45553	−	0.938839i	−0.840353	−	0.542039i
$3$	−1.45553	−	0.938839i	−0.840353	−	0.542039i
$4$	0.0960923	+	0.264011i	0.0480461	+	0.132006i
$5$		0			0
$5$		0			0
$6$	0.987435	+	2.42236i	0.403119	+	0.988925i
$7$	−0.677826	−	1.45360i	−0.256194	−	0.549410i	0.735576	−	0.677442i	$-0.236912\pi$
$7$	−0.677826	−	1.45360i	−0.256194	−	0.549410i	−0.991770	+	0.128032i	$0.959134\pi$
$8$	−0.671958	+	2.50778i	−0.237573	+	0.886634i
$9$	1.23716	+	2.73303i	0.412387	+	0.911009i
$10$		0			0
$11$	−1.78545	−	2.12782i	−0.538334	−	0.641561i	0.426479	−	0.904497i	$-0.359754\pi$
$11$	−1.78545	−	2.12782i	−0.538334	−	0.641561i	−0.964813	+	0.262936i	$0.915309\pi$
$12$	0.107999	−	0.474493i	0.0311765	−	0.136974i
$13$	−0.176418	−	0.251952i	−0.0489296	−	0.0698788i	0.793942	−	0.607994i	$-0.208025\pi$
$13$	−0.176418	−	0.251952i	−0.0489296	−	0.0698788i	−0.842871	+	0.538115i	$0.819137\pi$
$14$	−0.420628	+	2.38550i	−0.112418	+	0.637552i
$15$		0			0
$16$	3.43416	−	2.88160i	0.858539	−	0.720400i
$17$	1.88139	+	7.02145i	0.456304	+	1.70295i	0.684225	+	0.729271i	$0.260141\pi$
$17$	1.88139	+	7.02145i	0.456304	+	1.70295i	−0.227921	+	0.973680i	$0.573193\pi$
$18$	0.836964	−	4.45287i	0.197274	−	1.04955i
$19$	−5.07203	+	2.92834i	−1.16360	+	0.671807i	−0.952165	−	0.305584i	$-0.901148\pi$
$19$	−5.07203	+	2.92834i	−1.16360	+	0.671807i	−0.211439	+	0.977391i	$0.567815\pi$
$20$		0			0
$21$	−0.378100	+	2.75214i	−0.0825083	+	0.600566i
$22$	0.365624	+	4.17910i	0.0779514	+	0.890988i
$23$	−0.116642	−	0.0543910i	−0.0243215	−	0.0113413i	0.410419	−	0.911897i	$-0.365382\pi$
$23$	−0.116642	−	0.0543910i	−0.0243215	−	0.0113413i	−0.434741	+	0.900556i	$0.643160\pi$
$24$	3.33246	−	3.01930i	0.680236	−	0.616312i
$25$		0			0
$26$			0.464527i			0.0911012i
$27$	0.765143	−	5.13951i	0.147252	−	0.989099i
$28$	0.318634	−	0.318634i	0.0602161	−	0.0602161i
$29$	1.51659	+	8.60103i	0.281625	+	1.59717i	0.717099	+	0.696971i	$0.245469\pi$
$29$	1.51659	+	8.60103i	0.281625	+	1.59717i	−0.435475	+	0.900201i	$0.643419\pi$
$30$		0			0
$31$	4.22026	−	1.53605i	0.757981	−	0.275883i	0.0660211	−	0.997818i	$-0.478970\pi$
$31$	4.22026	−	1.53605i	0.757981	−	0.275883i	0.691960	+	0.721936i	$0.256747\pi$
$32$	−1.57207	+	0.137538i	−0.277905	+	0.0243135i
$33$	0.601106	+	4.77337i	0.104639	+	0.830936i
$34$	3.75485	−	10.3164i	0.643952	−	1.76924i
$35$		0			0
$36$	−0.602668	+	0.589247i	−0.100445	+	0.0982079i
$37$	−2.08386	+	0.558369i	−0.342585	+	0.0917953i	−0.426009	−	0.904719i	$-0.640081\pi$
$37$	−2.08386	+	0.558369i	−0.342585	+	0.0917953i	0.0834245	+	0.996514i	$0.473414\pi$
$38$	8.81158	+	0.770913i	1.42943	+	0.125059i
$39$	0.0202409	+	0.532353i	0.00324114	+	0.0852446i
$40$		0			0
$41$	−4.62442	−	0.815410i	−0.722213	−	0.127346i	−0.199553	−	0.979887i	$-0.563949\pi$
$41$	−4.62442	−	0.815410i	−0.722213	−	0.127346i	−0.522660	+	0.852541i	$0.675060\pi$
$42$	2.85184	−	3.07728i	0.440049	−	0.474834i
$43$	0.429127	−	4.90494i	0.0654412	−	0.747997i	−0.890604	−	0.454779i	$-0.849718\pi$
$43$	0.429127	−	4.90494i	0.0654412	−	0.747997i	0.956046	−	0.293218i	$-0.0947261\pi$
$44$	0.390200	−	0.675847i	0.0588249	−	0.101888i
$45$		0			0
$46$	0.0971868	+	0.168333i	0.0143294	+	0.0248193i
$47$	7.69135	−	3.58654i	1.12190	−	0.523150i	0.229009	−	0.973424i	$-0.426452\pi$
$47$	7.69135	−	3.58654i	1.12190	−	0.523150i	0.892890	+	0.450274i	$0.148674\pi$
$48$	−7.70389	+	0.970146i	−1.11196	+	0.140028i
$49$	2.84600	−	3.39173i	0.406571	−	0.484533i
$50$		0			0
$51$	3.85358	−	11.9863i	0.539609	−	1.67841i
$52$	0.0495656	−	0.0707870i	0.00687352	−	0.00981640i
$53$	−0.483003	−	0.483003i	−0.0663456	−	0.0663456i	0.673155	−	0.739501i	$-0.264938\pi$
$53$	−0.483003	−	0.483003i	−0.0663456	−	0.0663456i	−0.739501	+	0.673155i	$0.764938\pi$
$54$	−5.39876	+	5.69554i	−0.734679	+	0.775064i
$55$		0			0
$56$	4.10079	−	0.723079i	0.547991	−	0.0966255i
$57$	10.1318	+	0.499526i	1.34198	+	0.0661638i
$58$	5.57450	−	11.9546i	0.731968	−	1.56971i
$59$	7.43127	+	6.23558i	0.967469	+	0.811803i	0.982152	−	0.188089i	$-0.0602295\pi$
$59$	7.43127	+	6.23558i	0.967469	+	0.811803i	−0.0146830	+	0.999892i	$0.504674\pi$
$60$		0			0
$61$	2.50049	+	0.910105i	0.320155	+	0.116527i	0.497099	−	0.867694i	$-0.334399\pi$
$61$	2.50049	+	0.910105i	0.320155	+	0.116527i	−0.176943	+	0.984221i	$0.556621\pi$
$62$	−6.55173	−	1.75553i	−0.832070	−	0.222952i
$63$	3.13415	−	3.65086i	0.394866	−	0.459965i
$64$	−5.70071	−	3.29131i	−0.712589	−	0.411413i
$65$		0			0
$66$	3.39133	−	6.42609i	0.417444	−	0.790997i
$67$	0.884390	−	0.619257i	0.108045	−	0.0756543i	−0.518305	−	0.855196i	$-0.673437\pi$
$67$	0.884390	−	0.619257i	0.108045	−	0.0756543i	0.626350	+	0.779542i	$0.284548\pi$
$68$	−1.67295	+	1.17142i	−0.202876	+	0.142055i
$69$	0.118712	+	0.188676i	0.0142912	+	0.0227139i
$70$		0			0
$71$	9.03942	+	5.21891i	1.07278	+	0.619371i	0.928940	−	0.370230i	$-0.120721\pi$
$71$	9.03942	+	5.21891i	1.07278	+	0.619371i	0.143842	+	0.989601i	$0.454054\pi$
$72$	−7.68515	+	1.26605i	−0.905703	+	0.149205i
$73$	6.65047	+	1.78199i	0.778378	+	0.208566i	0.626070	−	0.779767i	$-0.284663\pi$
$73$	6.65047	+	1.78199i	0.778378	+	0.208566i	0.152309	+	0.988333i	$0.451329\pi$
$74$	3.06175	+	1.11439i	0.355921	+	0.129545i
$75$		0			0
$76$	−1.26050	−	1.05768i	−0.144589	−	0.121325i
$77$	−1.88278	+	4.03763i	−0.214562	+	0.460130i
$78$	0.436116	−	0.676135i	0.0493804	−	0.0765572i
$79$	2.04188	−	0.360038i	0.229729	−	0.0405074i	−0.0575985	−	0.998340i	$-0.518344\pi$
$79$	2.04188	−	0.360038i	0.229729	−	0.0405074i	0.287327	+	0.957832i	$0.407233\pi$
$80$		0			0
$81$	−5.93887	+	6.76239i	−0.659874	+	0.751376i
$82$	5.01475	+	5.01475i	0.553787	+	0.553787i
$83$	−7.55956	+	10.7962i	−0.829770	+	1.18503i	0.150742	+	0.988573i	$0.451834\pi$
$83$	−7.55956	+	10.7962i	−0.829770	+	1.18503i	−0.980512	+	0.196461i	$0.937055\pi$
$84$	−0.762929	+	0.164636i	−0.0832423	+	0.0179633i
$85$		0			0
$86$	−4.77986	+	5.69642i	−0.515426	+	0.614261i
$87$	5.86754	−	13.9429i	0.629066	−	1.49484i
$88$	6.53585	−	3.04772i	0.696724	−	0.324888i
$89$	−5.58181	−	9.66798i	−0.591671	−	1.02480i	−0.994007	−	0.109312i	$-0.965135\pi$
$89$	−5.58181	−	9.66798i	−0.591671	−	1.02480i	0.402337	−	0.915492i	$-0.368198\pi$
$90$		0			0
$91$	−0.246656	+	0.427222i	−0.0258566	+	0.0447850i
$92$	0.00315146	−	0.0360214i	0.000328562	−	0.00375549i
$93$	−7.58484	−	1.72638i	−0.786511	−	0.179017i
$94$	−12.6222	−	2.22564i	−1.30189	−	0.229558i
$95$		0			0
$96$	2.41732	+	1.27573i	0.246717	+	0.130203i
$97$	11.8062	+	1.03291i	1.19874	+	0.104876i	0.668986	−	0.743275i	$-0.266729\pi$
$97$	11.8062	+	1.03291i	1.19874	+	0.104876i	0.529754	+	0.848151i	$0.322284\pi$
$98$	−6.45906	+	1.73070i	−0.652464	+	0.174827i
$99$	3.60649	−	7.51214i	0.362466	−	0.754999i
$100$		0			0
$101$	−4.61138	+	12.6697i	−0.458850	+	1.26068i	0.467493	+	0.883997i	$0.345157\pi$
$101$	−4.61138	+	12.6697i	−0.458850	+	1.26068i	−0.926343	+	0.376682i	$0.877065\pi$
$102$	−15.1507	+	11.4906i	−1.50015	+	1.13774i
$103$	−2.96335	+	0.259260i	−0.291988	+	0.0255456i	−0.232209	−	0.972666i	$-0.574595\pi$
$103$	−2.96335	+	0.259260i	−0.291988	+	0.0255456i	−0.0597791	+	0.998212i	$0.519040\pi$
$104$	0.750384	−	0.273118i	0.0735813	−	0.0267814i
$105$		0			0
$106$	0.179140	+	1.01596i	0.0173997	+	0.0986783i
$107$	−7.80800	+	7.80800i	−0.754828	+	0.754828i	−0.975376	−	0.220548i	$-0.929215\pi$
$107$	−7.80800	+	7.80800i	−0.754828	+	0.754828i	0.220548	+	0.975376i	$0.429215\pi$
$108$	1.43041	−	0.291861i	0.137642	−	0.0280843i
$109$		−	0.464359i		−	0.0444775i	−0.999753	−	0.0222388i	$-0.992921\pi$
$109$		−	0.464359i		−	0.0444775i	0.999753	−	0.0222388i	$-0.00707940\pi$
$110$		0			0
$111$	3.55735	+	1.14369i	0.337649	+	0.108554i
$112$	−6.51646	−	3.03868i	−0.615748	−	0.287128i
$113$	−0.0417367	−	0.477053i	−0.00392626	−	0.0448774i	0.993979	−	0.109572i	$-0.0349481\pi$
$113$	−0.0417367	−	0.477053i	−0.00392626	−	0.0448774i	−0.997905	+	0.0646950i	$0.979393\pi$
$114$	−12.1018	−	9.39475i	−1.13344	−	0.879899i
$115$		0			0
$116$	−2.12504	+	1.22689i	−0.197305	+	0.113914i
$117$	0.470332	−	0.793861i	0.0434822	−	0.0733924i
$118$	−3.79196	−	14.1518i	−0.349078	−	1.30278i
$119$	8.93114	−	7.49411i	0.818716	−	0.686984i
$120$		0			0
$121$	0.570356	−	3.23465i	0.0518506	−	0.294059i
$122$	−2.30510	−	3.29202i	−0.208694	−	0.298046i
$123$	5.96547	+	5.52845i	0.537888	+	0.498483i
$124$	0.811069	+	0.966595i	0.0728362	+	0.0868028i
$125$		0			0
$126$	−7.04003	+	1.80166i	−0.627175	+	0.160505i
$127$	−3.48210	+	12.9954i	−0.308987	+	1.15315i	0.620473	+	0.784228i	$0.286941\pi$
$127$	−3.48210	+	12.9954i	−0.308987	+	1.15315i	−0.929459	+	0.368925i	$0.879726\pi$
$128$	5.53535	+	11.8706i	0.489260	+	1.04922i
$129$	−5.22956	+	6.73643i	−0.460437	+	0.593110i
$130$		0			0
$131$	−2.11500	−	5.81092i	−0.184788	−	0.507702i	0.812361	−	0.583155i	$-0.198182\pi$
$131$	−2.11500	−	5.81092i	−0.184788	−	0.507702i	−0.997149	+	0.0754528i	$0.975960\pi$
$132$	−1.20246	+	0.617383i	−0.104661	+	0.0537363i
$133$	7.69460	+	5.38781i	0.667206	+	0.467183i
$134$	−1.63056			−0.140859
$135$		0			0
$136$	−18.8725			−1.61830
$137$	6.04873	+	4.23537i	0.516778	+	0.361852i	0.802683	−	0.596406i	$-0.203405\pi$
$137$	6.04873	+	4.23537i	0.516778	+	0.361852i	−0.285905	+	0.958258i	$0.592294\pi$
$138$	0.0165784	−	0.336257i	0.00141125	−	0.0286241i
$139$	3.50715	+	9.63582i	0.297473	+	0.817299i	0.994921	+	0.100664i	$0.0320966\pi$
$139$	3.50715	+	9.63582i	0.297473	+	0.817299i	−0.697448	+	0.716635i	$0.745681\pi$
$140$		0			0
$141$	−14.5622	−	2.00062i	−1.22636	−	0.168482i
$142$	−6.66218	−	14.2871i	−0.559078	−	1.19895i
$143$	−0.221121	+	0.825233i	−0.0184910	+	0.0690095i
$144$	12.1241	+	5.82064i	1.01034	+	0.485053i
$145$		0			0
$146$	−6.68396	−	7.96564i	−0.553169	−	0.659241i
$147$	−7.32674	+	2.26484i	−0.604300	+	0.186801i
$148$	−0.347659	−	0.496508i	−0.0285774	−	0.0408127i
$149$	−0.210055	+	1.19128i	−0.0172084	+	0.0975937i	−0.992202	−	0.124638i	$-0.960223\pi$
$149$	−0.210055	+	1.19128i	−0.0172084	+	0.0975937i	0.974994	+	0.222232i	$0.0713341\pi$
$150$		0			0
$151$	−12.3858	+	10.3930i	−1.00795	+	0.845766i	−0.988065	−	0.154036i	$-0.950773\pi$
$151$	−12.3858	+	10.3930i	−1.00795	+	0.845766i	−0.0198800	+	0.999802i	$0.506328\pi$
$152$	−3.93544	−	14.6873i	−0.319206	−	1.19129i
$153$	−16.8622	+	13.8285i	−1.36323	+	1.11797i
$154$	5.82693	−	3.36418i	0.469547	−	0.271093i
$155$		0			0
$156$	−0.138602	+	0.0564988i	−0.0110971	+	0.00452353i
$157$	1.80822	+	20.6680i	0.144311	+	1.64949i	0.630907	+	0.775858i	$0.282683\pi$
$157$	1.80822	+	20.6680i	0.144311	+	1.64949i	−0.486596	+	0.873627i	$0.661762\pi$
$158$	−2.83800	−	1.32338i	−0.225779	−	0.105282i
$159$	0.249565	+	1.15649i	0.0197918	+	0.0917156i
$160$		0			0
$161$			0.206419i			0.0162681i
$162$	13.2053	−	3.22148i	1.03750	−	0.253103i
$163$	−9.24417	+	9.24417i	−0.724060	+	0.724060i	−0.969430	−	0.245370i	$-0.921091\pi$
$163$	−9.24417	+	9.24417i	−0.724060	+	0.724060i	0.245370	+	0.969430i	$0.421091\pi$
$164$	−0.229094	−	1.29925i	−0.0178892	−	0.101455i
$165$		0			0
$166$	18.7046	−	6.80794i	1.45176	−	0.528398i
$167$	−16.0301	+	1.40245i	−1.24044	+	0.108525i	−0.688425	−	0.725307i	$-0.741698\pi$
$167$	−16.0301	+	1.40245i	−1.24044	+	0.108525i	−0.552018	+	0.833832i	$0.686142\pi$
$168$	−6.64769	−	2.79751i	−0.512880	−	0.215833i
$169$	4.41391	−	12.1271i	0.339531	−	0.932854i
$170$		0			0
$171$	−14.2781	−	10.2392i	−1.09188	−	0.783009i
$172$	1.33620	−	0.358033i	0.101884	−	0.0272997i
$173$	2.64260	+	0.231197i	0.200913	+	0.0175776i	0.187168	−	0.982328i	$-0.440069\pi$
$173$	2.64260	+	0.231197i	0.200913	+	0.0175776i	0.0137449	+	0.999906i	$0.495625\pi$
$174$	−19.3373	+	12.1667i	−1.46596	+	0.922355i
$175$		0			0
$176$	−12.2630	−	2.16231i	−0.924362	−	0.162990i
$177$	−4.96226	−	16.0529i	−0.372987	−	1.20661i
$178$	−1.46947	+	16.7961i	−0.110141	+	1.25892i
$179$	−3.43088	+	5.94245i	−0.256436	+	0.444160i	−0.965284	−	0.261201i	$-0.915882\pi$
$179$	−3.43088	+	5.94245i	−0.256436	+	0.444160i	0.708849	+	0.705360i	$0.249215\pi$
$180$		0			0
$181$	10.0120	+	17.3412i	0.744183	+	1.28896i	0.950575	+	0.310494i	$0.100494\pi$
$181$	10.0120	+	17.3412i	0.744183	+	1.28896i	−0.206392	+	0.978469i	$0.566172\pi$
$182$	0.675238	−	0.314868i	0.0500519	−	0.0233396i
$183$	−2.78511	−	3.67225i	−0.205881	−	0.271460i
$184$	0.214779	−	0.255964i	0.0158337	−	0.0188699i
$185$		0			0
$186$	7.88810	+	8.70625i	0.578384	+	0.638373i
$187$	11.5812	−	16.5397i	0.846903	−	1.20950i
$188$	1.68597	+	1.68597i	0.122962	+	0.122962i
$189$	−7.98944	+	2.37148i	−0.581146	+	0.172500i
$190$		0			0
$191$	9.22577	−	1.62675i	0.667553	−	0.117708i	0.170406	−	0.985374i	$-0.445492\pi$
$191$	9.22577	−	1.62675i	0.667553	−	0.117708i	0.497147	+	0.867666i	$0.334381\pi$
$192$	5.20757	+	10.1427i	0.375824	+	0.731984i
$193$	−8.90711	+	19.1014i	−0.641148	+	1.37495i	0.269998	+	0.962861i	$0.412977\pi$
$193$	−8.90711	+	19.1014i	−0.641148	+	1.37495i	−0.911146	+	0.412085i	$0.864801\pi$
$194$	−13.7113	−	11.5052i	−0.984414	−	0.826022i
$195$		0			0
$196$	1.16893	+	0.425457i	0.0834953	+	0.0303898i
$197$	−7.09801	−	1.90191i	−0.505712	−	0.135505i	−0.00306257	−	0.999995i	$-0.500975\pi$
$197$	−7.09801	−	1.90191i	−0.505712	−	0.135505i	−0.502650	+	0.864490i	$0.667642\pi$
$198$	−10.9693	+	6.16948i	−0.779552	+	0.438446i
$199$	22.3449	+	12.9008i	1.58399	+	0.914516i	0.994269	+	0.106906i	$0.0340945\pi$
$199$	22.3449	+	12.9008i	1.58399	+	0.914516i	0.589718	+	0.807609i	$0.299239\pi$
$200$		0			0
$201$	−1.86864	+	0.0710490i	−0.131804	+	0.00501141i
$202$	16.6802	−	11.6796i	1.17362	−	0.821776i
$203$	11.4745	−	8.03453i	0.805352	−	0.563914i
$204$	3.53481	−	0.134400i	0.247486	−	0.00940985i
$205$		0			0
$206$	3.89070	+	2.24630i	0.271078	+	0.156507i
$207$	0.00434728	−	0.386076i	0.000302157	−	0.0268341i
$208$	−1.33187	−	0.356874i	−0.0923487	−	0.0247448i
$209$	15.2868	+	5.56395i	1.05741	+	0.384867i
$210$		0			0
$211$	−0.268205	−	0.225051i	−0.0184640	−	0.0154932i	0.633509	−	0.773735i	$-0.281614\pi$
$211$	−0.268205	−	0.225051i	−0.0184640	−	0.0154932i	−0.651973	+	0.758242i	$0.726058\pi$
$212$	0.0811054	−	0.173931i	0.00557035	−	0.0119456i
$213$	−8.25747	−	16.0829i	−0.565792	−	1.10198i
$214$	16.4235	−	2.89590i	1.12268	−	0.197960i
$215$		0			0
$216$	12.3746	+	5.37234i	0.841986	+	0.365542i
$217$	−5.09341	−	5.09341i	−0.345763	−	0.345763i
$218$	−0.402257	+	0.574483i	−0.0272443	+	0.0389089i
$219$	−8.00698	−	8.83746i	−0.541062	−	0.597180i
$220$		0			0
$221$	1.43715	−	1.71273i	0.0966733	−	0.115211i
$222$	−3.41025	−	4.49652i	−0.228881	−	0.301786i
$223$	14.2401	−	6.64028i	0.953590	−	0.444666i	0.117387	−	0.993086i	$-0.462548\pi$
$223$	14.2401	−	6.64028i	0.953590	−	0.444666i	0.836203	+	0.548420i	$0.184770\pi$
$224$	1.26551	+	2.19193i	0.0845557	+	0.146455i
$225$		0			0
$226$	−0.361618	+	0.626342i	−0.0240545	+	0.0416636i
$227$	2.05222	−	23.4570i	0.136211	−	1.55690i	−0.553522	−	0.832834i	$-0.686717\pi$
$227$	2.05222	−	23.4570i	0.136211	−	1.55690i	0.689733	−	0.724064i	$-0.257728\pi$
$228$	0.841703	+	2.72290i	0.0557431	+	0.180328i
$229$	−22.8004	−	4.02032i	−1.50669	−	0.265671i	−0.641505	−	0.767119i	$-0.721690\pi$
$229$	−22.8004	−	4.02032i	−1.50669	−	0.265671i	−0.865188	+	0.501448i	$0.832801\pi$
$230$		0			0
$231$	6.53113	−	4.10928i	0.429717	−	0.270371i
$232$	−22.5886	−	1.97625i	−1.48301	−	0.129747i
$233$	20.8931	−	5.59828i	1.36875	−	0.366755i	0.501728	−	0.865026i	$-0.332698\pi$
$233$	20.8931	−	5.59828i	1.36875	−	0.366755i	0.867022	+	0.498270i	$0.166031\pi$
$234$	−1.26956	+	0.574694i	−0.0829940	+	0.0375689i
$235$		0			0
$236$	−0.932175	+	2.56113i	−0.0606794	+	0.166715i
$237$	−3.31004	−	1.39295i	−0.215010	−	0.0904816i
$238$	−17.5410	+	1.53464i	−1.13702	+	0.0994761i
$239$	−13.3597	+	4.86252i	−0.864165	+	0.314530i	−0.735802	−	0.677197i	$-0.763195\pi$
$239$	−13.3597	+	4.86252i	−0.864165	+	0.314530i	−0.128363	+	0.991727i	$0.540972\pi$
$240$		0			0
$241$	−1.44826	−	8.21348i	−0.0932905	−	0.529077i	−0.995258	−	0.0972724i	$-0.968988\pi$
$241$	−1.44826	−	8.21348i	−0.0932905	−	0.529077i	0.901967	−	0.431804i	$-0.142123\pi$
$242$	−3.50767	+	3.50767i	−0.225482	+	0.225482i
$243$	14.9930	−	4.26724i	0.961803	−	0.273744i
$244$			0.747612i			0.0478610i
$245$		0			0
$246$	−2.59110	−	12.0072i	−0.165202	−	0.765550i
$247$	1.63260	+	0.761293i	0.103880	+	0.0484399i
$248$	1.01624	+	11.6156i	0.0645311	+	0.737594i
$249$	21.1391	−	8.61699i	1.33963	−	0.546079i
$250$		0			0
$251$	4.13040	−	2.38469i	0.260708	−	0.150520i	−0.363949	−	0.931419i	$-0.618572\pi$
$251$	4.13040	−	2.38469i	0.260708	−	0.150520i	0.624658	+	0.780899i	$0.285239\pi$
$252$	1.26504	+	0.476633i	0.0796898	+	0.0300251i
$253$	0.0925243	+	0.345305i	0.00581695	+	0.0217092i
$254$	15.5653	−	13.0608i	0.976654	−	0.819510i
$255$		0			0
$256$	1.14887	−	6.51557i	0.0718045	−	0.407223i
$257$	2.70759	+	3.86684i	0.168895	+	0.241207i	0.894673	−	0.446722i	$-0.147409\pi$
$257$	2.70759	+	3.86684i	0.168895	+	0.241207i	−0.725778	+	0.687929i	$0.758520\pi$
$258$	12.3053	−	3.80381i	0.766093	−	0.236815i
$259$	2.22414	+	2.65063i	0.138202	+	0.164702i
$260$		0			0
$261$	−21.6306	+	14.7858i	−1.33890	+	0.915215i
$262$	−2.41720	+	9.02113i	−0.149335	+	0.557327i
$263$	−1.40761	−	3.01862i	−0.0867967	−	0.186136i	0.858118	−	0.513452i	$-0.171634\pi$
$263$	−1.40761	−	3.01862i	−0.0867967	−	0.186136i	−0.944915	+	0.327316i	$0.893856\pi$
$264$	−12.3745	−	1.70006i	−0.761596	−	0.104631i
$265$		0			0
$266$	−4.85212	−	13.3311i	−0.297502	−	0.817381i
$267$	−0.952164	+	19.3125i	−0.0582715	+	1.18191i
$268$	0.248474	+	0.173983i	0.0151780	+	0.0106277i
$269$	−8.37429			−0.510589			−0.255295	−	0.966863i	$-0.582172\pi$
$269$	−8.37429			−0.510589			−0.255295	+	0.966863i	$0.582172\pi$
$270$		0			0
$271$	−13.7893			−0.837641			−0.418821	−	0.908069i	$-0.637556\pi$
$271$	−13.7893			−0.837641			−0.418821	+	0.908069i	$0.637556\pi$
$272$	26.6940	+	18.6913i	1.61856	+	1.13333i
$273$	0.760109	−	0.390265i	0.0460039	−	0.0236199i
$274$	−3.81425	−	10.4796i	−0.230428	−	0.633094i
$275$		0			0
$276$	−0.0384053	+	0.0494716i	−0.00231173	+	0.00297784i
$277$	−0.0519757	−	0.111462i	−0.00312292	−	0.00669711i	0.904740	−	0.425964i	$-0.140065\pi$
$277$	−0.0519757	−	0.111462i	−0.00312292	−	0.00669711i	−0.907863	+	0.419267i	$0.862287\pi$
$278$	4.00827	−	14.9591i	0.240400	−	0.897186i
$279$	9.41921	+	9.63375i	0.563913	+	0.576757i
$280$		0			0
$281$	15.4444	+	18.4059i	0.921334	+	1.09800i	0.994915	+	0.100714i	$0.0321127\pi$
$281$	15.4444	+	18.4059i	0.921334	+	1.09800i	−0.0735813	+	0.997289i	$0.523443\pi$
$282$	16.2826	+	15.0898i	0.969614	+	0.898582i
$283$	9.14396	+	13.0589i	0.543552	+	0.776273i	0.993136	−	0.116965i	$-0.0373166\pi$
$283$	9.14396	+	13.0589i	0.543552	+	0.776273i	−0.449584	+	0.893238i	$0.648428\pi$
$284$	−0.509233	+	2.88801i	−0.0302174	+	0.171372i
$285$		0			0
$286$	0.988429	−	0.829390i	0.0584470	−	0.0490429i
$287$	1.94927	+	7.27478i	0.115062	+	0.429417i
$288$	−2.32079	−	4.12634i	−0.136754	−	0.243147i
$289$	−31.0386	+	17.9202i	−1.82580	+	1.05413i
$290$		0			0
$291$	−16.2146	−	12.5876i	−0.950518	−	0.737897i
$292$	0.168594	+	1.92703i	0.00986619	+	0.112771i
$293$	4.77657	+	2.22735i	0.279050	+	0.130123i	0.557105	−	0.830442i	$-0.311912\pi$
$293$	4.77657	+	2.22735i	0.279050	+	0.130123i	−0.278055	+	0.960565i	$0.589690\pi$
$294$	11.0262	+	3.54493i	0.643063	+	0.206744i
$295$		0			0
$296$		−	5.60107i		−	0.325555i
$297$	−12.3021	+	7.54826i	−0.713838	+	0.437994i
$298$	1.29183	−	1.29183i	0.0748340	−	0.0748340i
$299$	0.00687388	+	0.0389837i	0.000397526	+	0.00225448i
$300$		0			0
$301$	−7.42071	+	2.70092i	−0.427723	+	0.155678i
$302$	24.3262	−	2.12827i	1.39981	−	0.122468i
$303$	18.6068	−	14.1118i	1.06893	−	0.810701i
$304$	−8.97985	+	24.6719i	−0.515030	+	1.41503i
$305$		0			0
$306$	32.8403	−	2.50090i	1.87735	−	0.142967i
$307$	21.3785	−	5.72834i	1.22013	−	0.326934i	0.409403	−	0.912353i	$-0.365737\pi$
$307$	21.3785	−	5.72834i	1.22013	−	0.326934i	0.810730	+	0.585420i	$0.199070\pi$
$308$	−1.24690	−	0.109090i	−0.0710487	−	0.00621596i
$309$	4.55666	+	2.40475i	0.259220	+	0.136801i
$310$		0			0
$311$	14.1711	+	2.49874i	0.803567	+	0.141691i	0.560322	−	0.828275i	$-0.310677\pi$
$311$	14.1711	+	2.49874i	0.803567	+	0.141691i	0.243244	+	0.969965i	$0.421788\pi$
$312$	−1.34862	−	0.306959i	−0.0763508	−	0.0173781i
$313$	1.85245	−	21.1736i	0.104707	−	1.19680i	−0.744088	−	0.668081i	$-0.767116\pi$
$313$	1.85245	−	21.1736i	0.104707	−	1.19680i	0.848795	−	0.528722i	$-0.177329\pi$
$314$	15.6669	−	27.1358i	0.884133	−	1.53136i
$315$		0			0
$316$	0.291263	+	0.504482i	0.0163848	+	0.0283793i
$317$	−20.8348	+	9.71542i	−1.17020	+	0.545672i	−0.907848	−	0.419300i	$-0.862275\pi$
$317$	−20.8348	+	9.71542i	−1.17020	+	0.545672i	−0.262350	+	0.964973i	$0.584498\pi$
$318$	0.693074	−	1.64694i	0.0388657	−	0.0923559i
$319$	15.5936	−	18.5838i	0.873076	−	1.04049i
$320$		0			0
$321$	18.6953	−	4.03435i	1.04347	−	0.225176i
$322$	0.178813	−	0.255371i	0.00996485	−	0.0142313i
$323$	−30.1036	−	30.1036i	−1.67501	−	1.67501i
$324$	−2.35603	−	0.918115i	−0.130890	−	0.0510064i
$325$		0			0
$326$	19.4443	−	3.42856i	1.07692	−	0.189890i
$327$	−0.435959	+	0.675891i	−0.0241086	+	0.0373768i
$328$	5.15228	−	11.0491i	0.284487	−	0.610085i
$329$	−10.4268	−	8.74912i	−0.574848	−	0.482355i
$330$		0			0
$331$	13.1133	+	4.77285i	0.720772	+	0.262340i	0.676253	−	0.736669i	$-0.263602\pi$
$331$	13.1133	+	4.77285i	0.720772	+	0.262340i	0.0445184	+	0.999009i	$0.485825\pi$
$332$	−3.57673	−	0.958382i	−0.196298	−	0.0525980i
$333$	−4.10411	−	5.00446i	−0.224904	−	0.274243i
$334$	21.0465	+	12.1512i	1.15161	+	0.664884i
$335$		0			0
$336$	6.63211	+	10.5408i	0.361811	+	0.575049i
$337$	−11.8702	+	8.31162i	−0.646612	+	0.452763i	−0.850318	−	0.526269i	$-0.823590\pi$
$337$	−11.8702	+	8.31162i	−0.646612	+	0.452763i	0.203705	+	0.979032i	$0.434701\pi$
$338$	−15.9659	+	11.1795i	−0.868432	+	0.608083i
$339$	−0.387127	+	0.733551i	−0.0210258	+	0.0398410i
$340$		0			0
$341$	−10.8035	−	6.23741i	−0.585043	−	0.337775i
$342$	8.79441	+	25.0360i	0.475547	+	1.35379i
$343$	−17.7039	−	4.74374i	−0.955920	−	0.256138i
$344$	12.0122	+	4.37207i	0.647652	+	0.235726i
$345$		0			0
$346$	−3.06901	−	2.57521i	−0.164991	−	0.138444i
$347$	3.83685	−	8.22815i	0.205973	−	0.441710i	−0.776000	−	0.630733i	$-0.782754\pi$
$347$	3.83685	−	8.22815i	0.205973	−	0.441710i	0.981973	+	0.189023i	$0.0605320\pi$
$348$	4.24492	+	0.209287i	0.227552	+	0.0112190i
$349$	8.20842	−	1.44737i	0.439387	−	0.0774757i	0.0504212	−	0.998728i	$-0.483944\pi$
$349$	8.20842	−	1.44737i	0.439387	−	0.0774757i	0.388966	+	0.921252i	$0.372833\pi$
$350$		0			0
$351$	−1.42989	+	0.713925i	−0.0763220	+	0.0381065i
$352$	3.09950	+	3.09950i	0.165204	+	0.165204i
$353$	1.51501	−	2.16366i	0.0806358	−	0.115160i	−0.776808	−	0.629738i	$-0.783162\pi$
$353$	1.51501	−	2.16366i	0.0806358	−	0.115160i	0.857444	+	0.514578i	$0.172051\pi$
$354$	−7.76693	+	24.1585i	−0.412808	+	1.28401i
$355$		0			0
$356$	2.01609	−	2.40268i	0.106852	−	0.127342i
$357$	−20.0353	+	2.52304i	−1.06038	+	0.133533i
$358$	9.39224	−	4.37967i	0.496395	−	0.231473i
$359$	−7.06131	−	12.2306i	−0.372682	−	0.645504i	0.617295	−	0.786732i	$-0.288228\pi$
$359$	−7.06131	−	12.2306i	−0.372682	−	0.645504i	−0.989977	+	0.141228i	$0.954895\pi$
$360$		0			0
$361$	7.65033	−	13.2508i	0.402649	−	0.697408i
$362$	2.63575	−	30.1267i	0.138532	−	1.58342i
$363$	−3.86699	+	4.17267i	−0.202964	+	0.219009i
$364$	−0.136493	−	0.0240674i	−0.00715418	−	0.00126148i
$365$		0			0
$366$	0.264470	+	6.95577i	0.0138241	+	0.363584i
$367$	13.7173	+	1.20011i	0.716037	+	0.0626451i	0.439351	−	0.898315i	$-0.355208\pi$
$367$	13.7173	+	1.20011i	0.716037	+	0.0626451i	0.276686	+	0.960961i	$0.410764\pi$
$368$	−0.557300	+	0.149328i	−0.0290513	+	0.00778426i
$369$	−3.49262	−	13.6475i	−0.181818	−	0.710458i
$370$		0			0
$371$	−0.374703	+	1.02949i	−0.0194536	+	0.0534483i
$372$	−0.273062	−	2.16838i	−0.0141576	−	0.112425i
$373$	20.2366	−	1.77048i	1.04781	−	0.0916718i	0.449777	−	0.893141i	$-0.351503\pi$
$373$	20.2366	−	1.77048i	1.04781	−	0.0916718i	0.598036	+	0.801469i	$0.295948\pi$
$374$	−28.6555	+	10.4297i	−1.48174	+	0.539309i
$375$		0			0
$376$	3.82598	+	21.6982i	0.197310	+	1.11900i
$377$	1.89949	−	1.89949i	0.0978286	−	0.0978286i
$378$	11.9385	+	3.98707i	0.614049	+	0.205073i
$379$			20.8542i			1.07121i	0.844469	+	0.535605i	$0.179916\pi$
$379$			20.8542i			1.07121i	−0.844469	+	0.535605i	$0.820084\pi$
$380$		0			0
$381$	17.2689	−	15.6461i	0.884712	−	0.801573i
$382$	−12.8229	−	5.97940i	−0.656075	−	0.305933i
$383$	−1.27835	−	14.6116i	−0.0653206	−	0.746618i	−0.956264	−	0.292504i	$-0.905512\pi$
$383$	−1.27835	−	14.6116i	−0.0653206	−	0.746618i	0.890944	−	0.454114i	$-0.150044\pi$
$384$	3.08769	−	22.4749i	0.157568	−	1.14692i
$385$		0			0
$386$	27.5662	−	15.9154i	1.40308	−	0.810071i
$387$	13.9362	−	4.89539i	0.708419	−	0.248847i
$388$	0.861786	+	3.21623i	0.0437506	+	0.163279i
$389$	−4.79561	+	4.02400i	−0.243147	+	0.204025i	−0.756215	−	0.654323i	$-0.772953\pi$
$389$	−4.79561	+	4.02400i	−0.243147	+	0.204025i	0.513067	+	0.858348i	$0.328509\pi$
$390$		0			0
$391$	0.162455	−	0.921326i	0.00821568	−	0.0465934i
$392$	6.59332	+	9.41624i	0.333013	+	0.475592i
$393$	−2.37706	+	10.4436i	−0.119907	+	0.526812i
$394$	7.13377	+	8.50169i	0.359394	+	0.428309i
$395$		0			0
$396$	2.32985	+	0.230297i	0.117079	+	0.0115728i
$397$	−0.120732	+	0.450577i	−0.00605935	+	0.0226138i	−0.968889	−	0.247494i	$-0.920393\pi$
$397$	−0.120732	+	0.450577i	−0.00605935	+	0.0226138i	0.962830	+	0.270108i	$0.0870595\pi$
$398$	−16.4685	−	35.3168i	−0.825492	−	1.77027i
$399$	−6.14146	−	15.0661i	−0.307457	−	0.754250i
$400$		0			0
$401$	3.19304	+	8.77280i	0.159453	+	0.438093i	0.993532	−	0.113552i	$-0.0362228\pi$
$401$	3.19304	+	8.77280i	0.159453	+	0.438093i	−0.834079	+	0.551644i	$0.814001\pi$
$402$	2.37334	+	1.53084i	0.118372	+	0.0763513i
$403$	−1.13154	−	0.792314i	−0.0563661	−	0.0394680i
$404$	−3.78805			−0.188463
$405$		0			0
$406$	−21.1557			−1.04994
$407$	4.90874	+	3.43714i	0.243317	+	0.170373i
$408$	27.4695	+	17.7182i	1.35994	+	0.877182i
$409$	−0.240362	−	0.660389i	−0.0118851	−	0.0326541i	0.933608	−	0.358296i	$-0.116642\pi$
$409$	−0.240362	−	0.660389i	−0.0118851	−	0.0326541i	−0.945493	+	0.325641i	$0.894420\pi$
$410$		0			0
$411$	−4.82780	−	11.8435i	−0.238138	−	0.584197i
$412$	−0.353203	−	0.757446i	−0.0174010	−	0.0373167i
$413$	4.02694	−	15.0288i	0.198153	−	0.739517i
$414$	−0.339821	+	0.473869i	−0.0167013	+	0.0232894i
$415$		0			0
$416$	0.311994	+	0.371820i	0.0152968	+	0.0182300i
$417$	3.94171	−	17.3179i	0.193026	−	0.848062i
$418$	−14.0923	−	20.1259i	−0.689276	−	0.984389i
$419$	−3.72329	+	21.1158i	−0.181894	+	1.03157i	0.747986	+	0.663714i	$0.231021\pi$
$419$	−3.72329	+	21.1158i	−0.181894	+	1.03157i	−0.929881	+	0.367861i	$0.880090\pi$
$420$		0			0
$421$	13.6486	−	11.4526i	0.665194	−	0.558164i	−0.246445	−	0.969157i	$-0.579262\pi$
$421$	13.6486	−	11.4526i	0.665194	−	0.558164i	0.911638	+	0.410993i	$0.134818\pi$
$422$	0.136857	+	0.510759i	0.00666211	+	0.0248633i
$423$	19.3175	+	16.5835i	0.939251	+	0.806319i
$424$	1.53582	−	0.886708i	0.0745862	−	0.0430623i
$425$		0			0
$426$	−3.71625	+	27.0501i	−0.180053	+	1.31058i
$427$	−0.371968	−	4.25162i	−0.0180008	−	0.205750i
$428$	−2.81169	−	1.31111i	−0.135908	−	0.0633750i
$429$	1.09661	−	0.993559i	0.0529449	−	0.0479695i
$430$		0			0
$431$			13.6942i			0.659624i	0.944047	+	0.329812i	$0.106985\pi$
$431$			13.6942i			0.659624i	−0.944047	+	0.329812i	$0.893015\pi$
$432$	−12.1824	−	19.8547i	−0.586126	−	0.955261i
$433$	−22.8337	+	22.8337i	−1.09732	+	1.09732i	−0.102594	+	0.994723i	$0.532714\pi$
$433$	−22.8337	+	22.8337i	−1.09732	+	1.09732i	−0.994723	+	0.102594i	$0.967286\pi$
$434$	1.88909	+	10.7136i	0.0906791	+	0.514267i
$435$		0			0
$436$	0.122596	−	0.0446213i	0.00587129	−	0.00213697i
$437$	0.750887	−	0.0656941i	0.0359198	−	0.00314257i
$438$	2.25028	+	17.8694i	0.107523	+	0.853834i
$439$	3.85214	−	10.5837i	0.183852	−	0.505130i	−0.813189	−	0.582000i	$-0.802270\pi$
$439$	3.85214	−	10.5837i	0.183852	−	0.505130i	0.997041	+	0.0768697i	$0.0244925\pi$
$440$		0			0
$441$	12.7907	+	3.58208i	0.609079	+	0.170575i
$442$	−3.26165	+	0.873956i	−0.155141	+	0.0415699i
$443$	−6.73147	−	0.588927i	−0.319822	−	0.0279808i	−0.0738853	−	0.997267i	$-0.523540\pi$
$443$	−6.73147	−	0.588927i	−0.319822	−	0.0279808i	−0.245936	+	0.969286i	$0.579095\pi$
$444$	0.0398878	+	1.04908i	0.00189299	+	0.0497872i
$445$		0			0
$446$	−23.3694	−	4.12066i	−1.10657	−	0.195119i
$447$	1.42417	−	1.53674i	0.0673607	−	0.0726855i
$448$	−0.920162	+	10.5175i	−0.0434736	+	0.496905i
$449$	−5.70190	+	9.87598i	−0.269089	+	0.466076i	−0.968627	−	0.248519i	$-0.920056\pi$
$449$	−5.70190	+	9.87598i	−0.269089	+	0.466076i	0.699538	+	0.714596i	$0.253389\pi$
$450$		0			0
$451$	6.52164	+	11.2958i	0.307092	+	0.531899i
$452$	0.121937	−	0.0568601i	0.00573542	−	0.00267447i
$453$	27.7853	−	3.49899i	1.30547	−	0.164397i
$454$	−22.8589	+	27.2421i	−1.07282	+	1.27854i
$455$		0			0
$456$	−8.06081	+	25.0725i	−0.377482	+	1.17413i
$457$	4.25450	−	6.07605i	0.199017	−	0.284226i	−0.707222	−	0.706992i	$-0.750052\pi$
$457$	4.25450	−	6.07605i	0.199017	−	0.284226i	0.906239	+	0.422766i	$0.138941\pi$
$458$	24.7249	+	24.7249i	1.15532	+	1.15532i
$459$	37.5263	−	4.29701i	1.75158	−	0.200567i
$460$		0			0
$461$	−41.0458	+	7.23749i	−1.91170	+	0.337083i	−0.997649	−	0.0685275i	$-0.978170\pi$
$461$	−41.0458	+	7.23749i	−1.91170	+	0.337083i	−0.914046	+	0.405611i	$0.867059\pi$
$462$	−11.6397	−	0.573873i	−0.541529	−	0.0266990i
$463$	−1.40671	+	3.01669i	−0.0653752	+	0.140198i	−0.936280	−	0.351253i	$-0.885756\pi$
$463$	−1.40671	+	3.01669i	−0.0653752	+	0.140198i	0.870905	+	0.491451i	$0.163533\pi$
$464$	29.9930	+	25.1671i	1.39239	+	1.16835i
$465$		0			0
$466$	−30.6975	−	11.1730i	−1.42203	−	0.517577i
$467$	4.32129	+	1.15789i	0.199966	+	0.0535806i	0.357412	−	0.933947i	$-0.383659\pi$
$467$	4.32129	+	1.15789i	0.199966	+	0.0535806i	−0.157446	+	0.987528i	$0.550326\pi$
$468$	0.254784	+	0.0478892i	0.0117774	+	0.00221368i
$469$	−1.49962	−	0.865804i	−0.0692458	−	0.0399791i
$470$		0			0
$471$	16.7720	−	31.7806i	0.772813	−	1.46437i
$472$	−20.6309	+	14.4459i	−0.949616	+	0.664929i
$473$	−11.2030	+	7.84443i	−0.515115	+	0.360687i
$474$	2.88836	+	4.59065i	0.132667	+	0.210855i
$475$		0			0
$476$	2.83674	+	1.63780i	0.130022	+	0.0750682i
$477$	0.722508	−	1.91761i	0.0330814	−	0.0878015i
$478$	20.7402	+	5.55731i	0.948632	+	0.254185i
$479$	−34.5314	−	12.5684i	−1.57778	−	0.574264i	−0.603059	−	0.797697i	$-0.706052\pi$
$479$	−34.5314	−	12.5684i	−1.57778	−	0.574264i	−0.974719	+	0.223432i	$0.928274\pi$
$480$		0			0
$481$	0.508314	+	0.426526i	0.0231771	+	0.0194479i
$482$	−5.32332	+	11.4159i	−0.242470	+	0.519980i
$483$	0.193794	−	0.300450i	0.00881793	−	0.0136709i
$484$	0.908792	−	0.160244i	0.0413087	−	0.00728384i
$485$		0			0
$486$	−22.2452	−	7.70867i	−1.00906	−	0.349672i
$487$	−9.05628	−	9.05628i	−0.410379	−	0.410379i	0.471492	−	0.881871i	$-0.343716\pi$
$487$	−9.05628	−	9.05628i	−0.410379	−	0.410379i	−0.881871	+	0.471492i	$0.843716\pi$
$488$	−3.96257	+	5.65913i	−0.179377	+	0.256177i
$489$	22.1340	−	4.77642i	1.00093	−	0.215997i
$490$		0			0
$491$	14.7648	−	17.5960i	0.666326	−	0.794096i	−0.321953	−	0.946756i	$-0.604339\pi$
$491$	14.7648	−	17.5960i	0.666326	−	0.794096i	0.988279	+	0.152660i	$0.0487838\pi$
$492$	−0.886338	+	2.10619i	−0.0399592	+	0.0949545i
$493$	−57.5384	+	26.8306i	−2.59140	+	1.20839i
$494$	−1.36029	−	2.35609i	−0.0612024	−	0.106006i
$495$		0			0
$496$	10.0668	−	17.4361i	0.452011	−	0.782906i
$497$	1.45907	−	16.6772i	0.0654482	−	0.748076i
$498$	−33.6168	−	7.65148i	−1.50641	−	0.342871i
$499$	−9.11992	−	1.60809i	−0.408264	−	0.0719879i	−0.0342550	−	0.999413i	$-0.510906\pi$
$499$	−9.11992	−	1.60809i	−0.408264	−	0.0719879i	−0.374009	+	0.927425i	$0.622017\pi$
$500$		0			0
$501$	24.6490	+	13.0083i	1.10124	+	0.581170i
$502$	−7.17569	−	0.627792i	−0.320267	−	0.0280197i
$503$	−8.31780	+	2.22875i	−0.370873	+	0.0993750i	−0.439441	−	0.898271i	$-0.644823\pi$
$503$	−8.31780	+	2.22875i	−0.370873	+	0.0993750i	0.0685686	+	0.997646i	$0.478157\pi$
$504$	7.04953	+	10.3130i	0.314011	+	0.459377i
$505$		0			0
$506$	0.184659	−	0.507345i	0.00820908	−	0.0225543i
$507$	−17.8100	+	13.5075i	−0.790970	+	0.599888i
$508$	−3.76553	+	0.329441i	−0.167068	+	0.0146166i
$509$	20.6614	−	7.52013i	0.915799	−	0.333324i	0.159233	−	0.987241i	$-0.449098\pi$
$509$	20.6614	−	7.52013i	0.915799	−	0.333324i	0.756566	+	0.653917i	$0.226876\pi$
$510$		0			0
$511$	−1.91756	−	10.8750i	−0.0848278	−	0.481082i
$512$	11.4575	−	11.4575i	0.506354	−	0.506354i
$513$	11.1694	+	28.3083i	0.493141	+	1.24984i
$514$		−	7.12936i		−	0.314463i
$515$		0			0
$516$	−2.28102	−	0.733345i	−0.100416	−	0.0322837i
$517$	−21.3640	−	9.96221i	−0.939589	−	0.438138i
$518$	−0.455459	−	5.20593i	−0.0200117	−	0.228735i
$519$	−3.62933	−	2.81749i	−0.159310	−	0.123674i
$520$		0			0
$521$	−4.43677	+	2.56157i	−0.194378	+	0.112224i	−0.594031	−	0.804442i	$-0.702464\pi$
$521$	−4.43677	+	2.56157i	−0.194378	+	0.112224i	0.399652	+	0.916667i	$0.369131\pi$
$522$	39.5687	+	0.445550i	1.73187	+	0.0195012i
$523$	−2.02890	−	7.57196i	−0.0887177	−	0.331099i	0.907275	−	0.420539i	$-0.138159\pi$
$523$	−2.02890	−	7.57196i	−0.0887177	−	0.331099i	−0.995992	+	0.0894400i	$0.971492\pi$
$524$	1.33091	−	1.11677i	0.0581412	−	0.0487863i
$525$		0			0
$526$	−0.873497	+	4.95385i	−0.0380863	+	0.215998i
$527$	18.7252	+	26.7424i	0.815685	+	1.16492i
$528$	15.8192	+	14.6603i	0.688443	+	0.638009i
$529$	−14.7735	−	17.6063i	−0.642325	−	0.765493i
$530$		0			0
$531$	−7.84832	+	28.0243i	−0.340588	+	1.21615i
$532$	−0.683053	+	2.54919i	−0.0296141	+	0.110521i
$533$	0.610389	+	1.30898i	0.0264389	+	0.0566984i
$534$	17.9077	−	23.0677i	0.774941	−	0.998236i
$535$		0			0
$536$	0.958687	+	2.63397i	0.0414090	+	0.113770i
$537$	10.5728	−	5.42840i	0.456248	−	0.234253i
$538$	10.3603	+	7.25433i	0.446663	+	0.312757i
$539$	−12.2984			−0.529729
$540$		0			0
$541$	−12.2903			−0.528401			−0.264200	−	0.964468i	$-0.585108\pi$
$541$	−12.2903			−0.528401			−0.264200	+	0.964468i	$0.585108\pi$
$542$	17.0595	+	11.9452i	0.732767	+	0.513089i
$543$	1.70787	−	34.6404i	0.0732919	−	1.48656i
$544$	−3.92339	−	10.7794i	−0.168214	−	0.462164i
$545$		0			0
$546$	−1.27844	−	0.175638i	−0.0547123	−	0.00751660i
$547$	0.220177	+	0.472172i	0.00941410	+	0.0201886i	0.910959	−	0.412498i	$-0.135344\pi$
$547$	0.220177	+	0.472172i	0.00941410	+	0.0201886i	−0.901545	+	0.432686i	$0.857566\pi$
$548$	−0.536948	+	2.00392i	−0.0229373	+	0.0856032i
$549$	0.606171	+	7.95986i	0.0258707	+	0.339718i
$550$		0			0
$551$	−32.8789	−	39.1836i	−1.40069	−	1.66928i
$552$	−0.552927	+	0.170921i	−0.0235342	+	0.00727488i
$553$	−1.90739	−	2.72403i	−0.0811104	−	0.115838i
$554$	−0.0322538	+	0.182920i	−0.00137033	+	0.00777153i
$555$		0			0
$556$	−2.20695	+	1.85185i	−0.0935957	+	0.0785361i
$557$	−6.03527	−	22.5239i	−0.255723	−	0.954370i	−0.967687	−	0.252155i	$-0.918861\pi$
$557$	−6.03527	−	22.5239i	−0.255723	−	0.954370i	0.711964	−	0.702216i	$-0.247806\pi$
$558$	−3.30763	−	20.0779i	−0.140023	−	0.849966i
$559$	−1.31151	+	0.757203i	−0.0554711	+	0.0320263i
$560$		0			0
$561$	−32.3850	+	13.2012i	−1.36730	+	0.557355i
$562$	−3.16269	−	36.1498i	−0.133410	−	1.52489i
$563$	−31.1449	−	14.5231i	−1.31260	−	0.612076i	−0.364844	−	0.931069i	$-0.618878\pi$
$563$	−31.1449	−	14.5231i	−1.31260	−	0.612076i	−0.947757	+	0.318993i	$0.896656\pi$
$564$	−0.871130	−	4.03683i	−0.0366812	−	0.169981i
$565$		0			0
$566$		−	24.0770i		−	1.01203i
$567$	13.8553	+	4.04903i	0.581870	+	0.170043i
$568$	−19.1620	+	19.1620i	−0.804019	+	0.804019i
$569$	0.227444	+	1.28990i	0.00953495	+	0.0540754i	0.989204	−	0.146545i	$-0.0468153\pi$
$569$	0.227444	+	1.28990i	0.00953495	+	0.0540754i	−0.979669	+	0.200620i	$0.935704\pi$
$570$		0			0
$571$	−17.9969	+	6.55033i	−0.753146	+	0.274123i	−0.689929	−	0.723877i	$-0.742358\pi$
$571$	−17.9969	+	6.55033i	−0.753146	+	0.274123i	−0.0632171	+	0.998000i	$0.520136\pi$
$572$	−0.239119	+	0.0209202i	−0.00999807	+	0.000874718i
$573$	−14.9557	−	6.29372i	−0.624782	−	0.262924i
$574$	3.89033	−	10.6886i	0.162379	−	0.446133i
$575$		0			0
$576$	1.94253	−	19.6521i	0.0809389	−	0.818836i
$577$	12.6473	−	3.38883i	0.526514	−	0.141079i	0.0142358	−	0.999899i	$-0.495468\pi$
$577$	12.6473	−	3.38883i	0.526514	−	0.141079i	0.512278	+	0.858820i	$0.328802\pi$
$578$	53.9231	+	4.71766i	2.24290	+	0.196229i
$579$	30.8977	−	19.4403i	1.28406	−	0.807913i
$580$		0			0
$581$	20.8174	+	3.67067i	0.863652	+	0.152285i
$582$	9.15579	+	29.6189i	0.379520	+	1.22774i
$583$	−0.165364	+	1.89012i	−0.00684869	+	0.0782808i
$584$	−8.93766	+	15.4805i	−0.369843	+	0.640587i
$585$		0			0
$586$	−3.97987	−	6.89333i	−0.164407	−	0.284761i
$587$	−26.3137	+	12.2703i	−1.08608	+	0.506449i	−0.881396	−	0.472379i	$-0.843395\pi$
$587$	−26.3137	+	12.2703i	−1.08608	+	0.506449i	−0.204687	+	0.978827i	$0.565618\pi$
$588$	−1.30199	−	1.71671i	−0.0536931	−	0.0707959i
$589$	−16.9072	+	20.1492i	−0.696650	+	0.830235i
$590$		0			0
$591$	8.54582	+	9.43219i	0.351528	+	0.387988i
$592$	−5.54732	+	7.92239i	−0.227993	+	0.325608i
$593$	18.8092	+	18.8092i	0.772402	+	0.772402i	0.978526	−	0.206124i	$-0.0660851\pi$
$593$	18.8092	+	18.8092i	0.772402	+	0.772402i	−0.206124	+	0.978526i	$0.566085\pi$
$594$	21.7583	+	1.31848i	0.892754	+	0.0540980i
$595$		0			0
$596$	−0.334697	+	0.0590161i	−0.0137097	+	0.00241739i
$597$	−20.4120	−	39.7559i	−0.835406	−	1.62710i
$598$	0.0252661	−	0.0541833i	0.00103321	−	0.00221572i
$599$	3.51169	+	2.94665i	0.143484	+	0.120397i	0.711704	−	0.702479i	$-0.247924\pi$
$599$	3.51169	+	2.94665i	0.143484	+	0.120397i	−0.568221	+	0.822876i	$0.692368\pi$
$600$		0			0
$601$	25.1131	+	9.14041i	1.02438	+	0.372845i	0.798940	−	0.601411i	$-0.205395\pi$
$601$	25.1131	+	9.14041i	1.02438	+	0.372845i	0.225443	+	0.974256i	$0.427617\pi$
$602$	11.5202	+	3.08684i	0.469530	+	0.125810i
$603$	2.78658	+	1.65094i	0.113478	+	0.0672316i
$604$	−3.93404	−	2.27132i	−0.160074	−	0.0924187i
$605$		0			0
$606$	−35.2440	+	1.34003i	−1.43169	+	0.0544352i
$607$	−29.2803	+	20.5023i	−1.18845	+	0.832163i	−0.989025	−	0.147749i	$-0.952797\pi$
$607$	−29.2803	+	20.5023i	−1.18845	+	0.832163i	−0.199428	+	0.979913i	$0.563908\pi$
$608$	7.57081	−	5.30114i	0.307037	−	0.214990i
$609$	−24.2447	+	0.921823i	−0.982443	+	0.0373542i
$610$		0			0
$611$	−2.26053	−	1.30512i	−0.0914512	−	0.0527994i
$612$	−5.27122	−	3.12300i	−0.213077	−	0.126240i
$613$	35.8682	+	9.61085i	1.44870	+	0.388179i	0.895572	−	0.444916i	$-0.146767\pi$
$613$	35.8682	+	9.61085i	1.44870	+	0.388179i	0.553130	+	0.833095i	$0.313433\pi$
$614$	−31.4107	−	11.4325i	−1.26763	−	0.461380i
$615$		0			0
$616$	−8.86034	−	7.43471i	−0.356993	−	0.299553i
$617$	−19.6545	+	42.1491i	−0.791258	+	1.69686i	−0.0769428	+	0.997036i	$0.524516\pi$
$617$	−19.6545	+	42.1491i	−0.791258	+	1.69686i	−0.714316	+	0.699824i	$0.753262\pi$
$618$	−3.55414	−	6.92231i	−0.142968	−	0.278456i
$619$	−13.9352	+	2.45716i	−0.560104	+	0.0987615i	−0.446531	−	0.894768i	$-0.647341\pi$
$619$	−13.9352	+	2.45716i	−0.560104	+	0.0987615i	−0.113573	+	0.993530i	$0.536230\pi$
$620$		0			0
$621$	−0.368791	+	0.557865i	−0.0147991	+	0.0223864i
$622$	−15.3672	−	15.3672i	−0.616168	−	0.616168i
$623$	−10.2699	+	14.6669i	−0.411455	+	0.587619i
$624$	1.60354	+	1.76986i	0.0641929	+	0.0708510i
$625$		0			0
$626$	−20.6337	+	24.5903i	−0.824687	+	0.982824i
$627$	−17.0269	−	22.4504i	−0.679987	−	0.896583i
$628$	−5.28283	+	2.46342i	−0.210808	+	0.0983013i
$629$	−7.84112	−	13.5812i	−0.312646	−	0.541519i
$630$		0			0
$631$	16.2979	−	28.2288i	0.648810	−	1.12377i	−0.334597	−	0.942361i	$-0.608600\pi$
$631$	16.2979	−	28.2288i	0.648810	−	1.12377i	0.983407	−	0.181411i	$-0.0580664\pi$
$632$	−0.469158	+	5.36250i	−0.0186621	+	0.213309i
$633$	0.179095	+	0.579371i	0.00711840	+	0.0230279i
$634$	34.1919	+	6.02895i	1.35793	+	0.239440i
$635$		0			0
$636$	−0.281345	+	0.177018i	−0.0111561	+	0.00701921i
$637$	−1.35664	−	0.118690i	−0.0537520	−	0.00470269i
$638$	−35.3901	+	9.48275i	−1.40111	+	0.375426i
$639$	−3.08021	+	31.1616i	−0.121851	+	1.23273i
$640$		0			0
$641$	−11.8689	+	32.6096i	−0.468794	+	1.28800i	0.449916	+	0.893071i	$0.351454\pi$
$641$	−11.8689	+	32.6096i	−0.468794	+	1.28800i	−0.918711	+	0.394931i	$0.870768\pi$
$642$	−26.6237	−	11.2039i	−1.05075	−	0.442183i
$643$	−8.82626	+	0.772198i	−0.348074	+	0.0304525i	−0.259852	−	0.965648i	$-0.583674\pi$
$643$	−8.82626	+	0.772198i	−0.348074	+	0.0304525i	−0.0882215	+	0.996101i	$0.528118\pi$
$644$	−0.0544969	+	0.0198352i	−0.00214748	+	0.000781618i
$645$		0			0
$646$	11.1651	+	63.3204i	0.439285	+	2.49131i
$647$	14.1426	−	14.1426i	0.556003	−	0.556003i	−0.372164	−	0.928167i	$-0.621384\pi$
$647$	14.1426	−	14.1426i	0.556003	−	0.556003i	0.928167	+	0.372164i	$0.121384\pi$
$648$	−12.9679	−	19.4374i	−0.509428	−	0.763573i
$649$		−	26.9457i		−	1.05771i
$650$		0			0
$651$	2.63174	+	12.1955i	0.103146	+	0.477980i
$652$	−3.32886	−	1.55227i	−0.130368	−	0.0607917i
$653$	0.173231	+	1.98004i	0.00677904	+	0.0774848i	0.998831	−	0.0483474i	$-0.0153955\pi$
$653$	0.173231	+	1.98004i	0.00677904	+	0.0774848i	−0.992052	+	0.125832i	$0.959840\pi$
$654$	1.12485	−	0.458524i	0.0439850	−	0.0179297i
$655$		0			0
$656$	−18.2307	+	10.5255i	−0.711788	+	0.410951i
$657$	3.35748	+	20.3805i	0.130988	+	0.795119i
$658$	5.32049	+	19.8563i	0.207414	+	0.774081i
$659$	−9.93910	+	8.33989i	−0.387172	+	0.324876i	−0.815510	−	0.578742i	$-0.803544\pi$
$659$	−9.93910	+	8.33989i	−0.387172	+	0.324876i	0.428338	+	0.903619i	$0.359099\pi$
$660$		0			0
$661$	2.91716	−	16.5440i	0.113464	−	0.643489i	−0.874035	−	0.485864i	$-0.838505\pi$
$661$	2.91716	−	16.5440i	0.113464	−	0.643489i	0.987499	−	0.157625i	$-0.0503837\pi$
$662$	−12.0886	−	17.2643i	−0.469836	−	0.670996i
$663$	−3.69980	+	1.14368i	−0.143688	+	0.0444170i
$664$	−21.9947	−	26.2123i	−0.853561	−	1.01723i
$665$		0			0
$666$	0.742231	+	9.74651i	0.0287609	+	0.377670i
$667$	0.290921	−	1.08573i	0.0112645	−	0.0420396i
$668$	−1.91063	−	4.09735i	−0.0739244	−	0.158531i
$669$	−26.9612	−	3.70404i	−1.04238	−	0.143206i
$670$		0			0
$671$	−2.52797	−	6.94554i	−0.0975912	−	0.268130i
$672$	0.215875	−	4.37855i	0.00832758	−	0.168906i
$673$	−7.48390	−	5.24028i	−0.288483	−	0.201998i	0.420373	−	0.907352i	$-0.361899\pi$
$673$	−7.48390	−	5.24028i	−0.288483	−	0.201998i	−0.708856	+	0.705353i	$0.750788\pi$
$674$	21.8853			0.842991
$675$		0			0
$676$	3.62584			0.139455
$677$	0.0991212	+	0.0694054i	0.00380954	+	0.00266747i	0.575480	−	0.817816i	$-0.304815\pi$
$677$	0.0991212	+	0.0694054i	0.00380954	+	0.00266747i	−0.571670	+	0.820484i	$0.693704\pi$
$678$	1.11438	−	0.572160i	0.0427976	−	0.0219737i
$679$	−6.50112	−	17.8617i	−0.249490	−	0.685468i
$680$		0			0
$681$	−25.0095	+	32.2158i	−0.958365	+	1.23451i
$682$	7.96234	+	17.0753i	0.304894	+	0.653847i
$683$	−3.58403	+	13.3758i	−0.137139	+	0.511810i	0.862841	+	0.505476i	$0.168683\pi$
$683$	−3.58403	+	13.3758i	−0.137139	+	0.511810i	−0.999980	+	0.00633429i	$0.997984\pi$
$684$	1.33124	−	4.75350i	0.0509011	−	0.181755i
$685$		0			0
$686$	17.7931	+	21.2049i	0.679342	+	0.809608i
$687$	29.4123	+	27.2576i	1.12215	+	1.03994i
$688$	−12.6604	−	18.0809i	−0.482673	−	0.689329i
$689$	−0.0364828	+	0.206904i	−0.00138988	+	0.00788241i
$690$		0			0
$691$	17.4891	−	14.6751i	0.665315	−	0.558266i	−0.246359	−	0.969179i	$-0.579234\pi$
$691$	17.4891	−	14.6751i	0.665315	−	0.558266i	0.911675	+	0.410913i	$0.134790\pi$
$692$	0.192894	+	0.719892i	0.00733274	+	0.0273662i
$693$	−13.3642	−	0.150484i	−0.507666	−	0.00571640i
$694$	−11.8745	+	6.85575i	−0.450750	+	0.260241i
$695$		0			0
$696$	31.0231	+	24.0835i	1.17593	+	0.912885i
$697$	−2.97498	−	34.0042i	−0.112686	−	1.28800i
$698$	−11.4089	−	5.32004i	−0.431832	−	0.201366i
$699$	−35.6664	−	11.4667i	−1.34903	−	0.433712i
$700$		0			0
$701$		−	15.6693i		−	0.591821i	−0.955216	−	0.295910i	$-0.904377\pi$
$701$		−	15.6693i		−	0.591821i	0.955216	−	0.295910i	$-0.0956230\pi$
$702$	2.38744	+	0.355429i	0.0901081	+	0.0134148i
$703$	8.93432	−	8.93432i	0.336964	−	0.336964i
$704$	3.17504	+	18.0065i	0.119664	+	0.678647i
$705$		0			0
$706$	−3.74859	+	1.36438i	−0.141080	+	0.0513490i
$707$	21.5424	−	1.88471i	0.810184	−	0.0708820i
$708$	3.76130	−	2.85265i	0.141358	−	0.107209i
$709$	−2.91839	+	8.01821i	−0.109602	+	0.301130i	−0.982353	−	0.187036i	$-0.940112\pi$
$709$	−2.91839	+	8.01821i	−0.109602	+	0.301130i	0.872751	+	0.488166i	$0.162334\pi$
$710$		0			0
$711$	3.51012	+	5.13508i	0.131640	+	0.192580i
$712$	27.9959	−	7.50148i	1.04919	−	0.281130i
$713$	−0.575807	−	0.0503766i	−0.0215641	−	0.00188662i
$714$	26.9724	+	14.2345i	1.00942	+	0.532713i
$715$		0			0
$716$	−1.89856	−	0.334767i	−0.0709523	−	0.0125108i
$717$	24.0106	+	5.46502i	0.896692	+	0.204095i
$718$	−1.85896	+	21.2480i	−0.0693758	+	0.792968i
$719$	19.9277	−	34.5157i	0.743176	−	1.28722i	−0.207866	−	0.978157i	$-0.566652\pi$
$719$	19.9277	−	34.5157i	0.743176	−	1.28722i	0.951042	−	0.309062i	$-0.100015\pi$
$720$		0			0
$721$	2.38550	+	4.13180i	0.0888406	+	0.153876i
$722$	−20.9433	+	9.76600i	−0.779427	+	0.363453i
$723$	−5.60315	+	13.3147i	−0.208383	+	0.495178i
$724$	−3.61621	+	4.30963i	−0.134395	+	0.160166i
$725$		0			0
$726$	8.39869	−	1.81240i	0.311704	−	0.0672644i
$727$	−26.2725	+	37.5210i	−0.974393	+	1.39158i	−0.0548911	+	0.998492i	$0.517481\pi$
$727$	−26.2725	+	37.5210i	−0.974393	+	1.39158i	−0.919502	+	0.393085i	$0.871408\pi$
$728$	−0.905635	−	0.905635i	−0.0335651	−	0.0335651i
$729$	−25.8291	−	7.86492i	−0.956634	−	0.291293i
$730$		0			0
$731$	35.2471	−	6.21502i	1.30366	−	0.229871i
$732$	0.701888	−	1.08818i	0.0259425	−	0.0402201i
$733$	15.6365	−	33.5325i	0.577546	−	1.23855i	−0.372961	−	0.927847i	$-0.621657\pi$
$733$	15.6365	−	33.5325i	0.577546	−	1.23855i	0.950507	−	0.310704i	$-0.100565\pi$
$734$	−15.9308	−	13.3675i	−0.588015	−	0.493403i
$735$		0			0
$736$	0.190850	+	0.0694636i	0.00703481	+	0.00256046i
$737$	−2.89670	−	0.776169i	−0.106701	−	0.0285906i
$738$	−7.50139	+	19.9095i	−0.276130	+	0.732879i
$739$	−9.45965	−	5.46153i	−0.347979	−	0.200906i	0.315816	−	0.948820i	$-0.397722\pi$
$739$	−9.45965	−	5.46153i	−0.347979	−	0.200906i	−0.663795	+	0.747915i	$0.731055\pi$
$740$		0			0
$741$	−1.66157	−	2.64084i	−0.0610393	−	0.0970135i
$742$	1.35537	−	0.949040i	0.0497572	−	0.0348404i
$743$	6.78635	−	4.75185i	0.248967	−	0.174329i	−0.442431	−	0.896802i	$-0.645884\pi$
$743$	6.78635	−	4.75185i	0.248967	−	0.174329i	0.691398	+	0.722474i	$0.256995\pi$
$744$	9.42606	−	17.8611i	0.345576	−	0.654818i
$745$		0			0
$746$	−26.5695	−	15.3399i	−0.972778	−	0.561633i
$747$	−38.8586	−	7.30388i	−1.42176	−	0.267235i
$748$	5.47954	+	1.46824i	0.200352	+	0.0536841i
$749$	16.6422	+	6.05726i	0.608093	+	0.221328i
$750$		0			0
$751$	1.01418	+	0.851000i	0.0370080	+	0.0310534i	0.661104	−	0.750294i	$-0.270088\pi$
$751$	1.01418	+	0.851000i	0.0370080	+	0.0310534i	−0.624096	+	0.781348i	$0.714533\pi$
$752$	16.0783	−	34.4801i	0.586317	−	1.25736i
$753$	−8.25077	−	0.406788i	−0.300675	−	0.0148242i
$754$	−3.99541	+	0.704499i	−0.145504	+	0.0256563i
$755$		0			0
$756$	−1.39382	−	1.88142i	−0.0506928	−	0.0684267i
$757$	26.5719	+	26.5719i	0.965772	+	0.965772i	0.999433	−	0.0336615i	$-0.0107168\pi$
$757$	26.5719	+	26.5719i	0.965772	+	0.965772i	−0.0336615	+	0.999433i	$0.510717\pi$
$758$	18.0652	−	25.7998i	0.656159	−	0.937092i
$759$	0.189514	−	0.589469i	0.00687892	−	0.0213964i
$760$		0			0
$761$	6.97127	−	8.30804i	0.252708	−	0.301166i	−0.624744	−	0.780829i	$-0.714797\pi$
$761$	6.97127	−	8.30804i	0.252708	−	0.301166i	0.877453	+	0.479663i	$0.159241\pi$
$762$	−34.9179	+	4.39718i	−1.26494	+	0.159293i
$763$	−0.674994	+	0.314755i	−0.0244364	+	0.0113949i
$764$	1.31601	+	2.27939i	0.0476114	+	0.0824654i
$765$		0			0
$766$	−11.0760	+	19.1841i	−0.400191	+	0.693151i
$767$	0.260050	−	2.97239i	0.00938988	−	0.107327i
$768$	−7.78930	+	8.40504i	−0.281072	+	0.303291i
$769$	44.1842	+	7.79087i	1.59332	+	0.280946i	0.898745	−	0.438471i	$-0.144480\pi$
$769$	44.1842	+	7.79087i	1.59332	+	0.280946i	0.694579	+	0.719417i	$0.255591\pi$
$770$		0			0
$771$	−0.310649	−	8.17032i	−0.0111878	−	0.294247i
$772$	−5.89888	−	0.516085i	−0.212305	−	0.0185743i
$773$	30.3757	−	8.13915i	1.09254	−	0.292745i	0.332816	−	0.942992i	$-0.392001\pi$
$773$	30.3757	−	8.13915i	1.09254	−	0.292745i	0.759723	+	0.650247i	$0.225334\pi$
$774$	−21.4819	−	6.01611i	−0.772152	−	0.216244i
$775$		0			0
$776$	−10.5236	+	28.9133i	−0.377775	+	1.03793i
$777$	−0.748800	−	5.94620i	−0.0268631	−	0.213319i
$778$	9.41874	−	0.824033i	0.337678	−	0.0295430i
$779$	25.8430	−	9.40608i	0.925922	−	0.337008i
$780$		0			0
$781$	−5.03455	−	28.5524i	−0.180150	−	1.02168i
$782$	−0.999091	+	0.999091i	−0.0357274	+	0.0357274i
$783$	45.3655	−	1.21353i	1.62123	−	0.0433680i
$784$		−	19.8488i		−	0.708885i
$785$		0			0
$786$	11.9877	−	10.8612i	0.427588	−	0.387406i
$787$	28.5680	+	13.3215i	1.01834	+	0.474860i	0.858789	−	0.512330i	$-0.171217\pi$
$787$	28.5680	+	13.3215i	1.01834	+	0.474860i	0.159552	+	0.987190i	$0.448995\pi$
$788$	−0.179939	−	2.05671i	−0.00641007	−	0.0732674i
$789$	−0.785181	+	5.71522i	−0.0279532	+	0.203467i
$790$		0			0
$791$	−0.665155	+	0.384027i	−0.0236502	+	0.0136544i
$792$	16.4154	+	14.0921i	0.583295	+	0.500742i
$793$	−0.211830	−	0.790562i	−0.00752232	−	0.0280737i
$794$	0.539681	−	0.452846i	0.0191526	−	0.0160709i
$795$		0			0
$796$	−1.25879	+	7.13898i	−0.0446168	+	0.253034i
$797$	3.73721	+	5.33729i	0.132379	+	0.189057i	0.879869	−	0.475216i	$-0.157630\pi$
$797$	3.73721	+	5.33729i	0.132379	+	0.189057i	−0.747490	+	0.664273i	$0.768741\pi$
$798$	−5.45332	+	23.9592i	−0.193046	+	0.848147i
$799$	39.6531	+	47.2567i	1.40283	+	1.67182i
$800$		0			0
$801$	19.5173	−	27.2161i	0.689608	−	0.961633i
$802$	3.64928	−	13.6193i	0.128860	−	0.480914i
$803$	−8.08234	−	17.3326i	−0.285220	−	0.611655i
$804$	−0.198320	−	0.486516i	−0.00699421	−	0.0171581i
$805$		0			0
$806$	0.713536	+	1.96042i	0.0251332	+	0.0690530i
$807$	12.1891	+	7.86211i	0.429075	+	0.276759i
$808$	−28.6741	−	20.0778i	−1.00875	−	0.706335i
$809$	−21.5117			−0.756312			−0.378156	−	0.925742i	$-0.623442\pi$
$809$	−21.5117			−0.756312			−0.378156	+	0.925742i	$0.623442\pi$
$810$		0			0
$811$	15.2216			0.534502			0.267251	−	0.963627i	$-0.413885\pi$
$811$	15.2216			0.534502			0.267251	+	0.963627i	$0.413885\pi$
$812$	3.22382	+	2.25734i	0.113134	+	0.0792172i
$813$	20.0708	+	12.9460i	0.703914	+	0.454034i
$814$	−3.09539	−	8.50453i	−0.108494	−	0.298083i
$815$		0			0
$816$	−21.3059	−	52.2673i	−0.745854	−	1.82972i
$817$	12.1868	+	26.1346i	0.426362	+	0.914335i
$818$	−0.274706	+	1.02522i	−0.00960488	+	0.0358459i
$819$	−1.47276	−	0.145577i	−0.0514624	−	0.00508687i
$820$		0			0
$821$	−32.2494	−	38.4334i	−1.12551	−	1.34133i	−0.932932	−	0.360053i	$-0.882758\pi$
$821$	−32.2494	−	38.4334i	−1.12551	−	1.34133i	−0.192581	−	0.981281i	$-0.561686\pi$
$822$	−4.28686	+	18.8344i	−0.149522	+	0.656924i
$823$	−2.01204	−	2.87349i	−0.0701354	−	0.100164i	0.782552	−	0.622585i	$-0.213918\pi$
$823$	−2.01204	−	2.87349i	−0.0701354	−	0.100164i	−0.852687	+	0.522422i	$0.825029\pi$
$824$	1.34108	−	7.60564i	0.0467187	−	0.264955i
$825$		0			0
$826$	−18.0008	+	15.1045i	−0.626327	+	0.525551i
$827$	−0.686704	−	2.56281i	−0.0238790	−	0.0891178i	0.952958	−	0.303102i	$-0.0980224\pi$
$827$	−0.686704	−	2.56281i	−0.0238790	−	0.0891178i	−0.976837	+	0.213985i	$0.931356\pi$
$828$	0.102346	−	0.0359512i	0.00355678	−	0.00124939i
$829$	13.2911	−	7.67359i	0.461617	−	0.266515i	−0.251107	−	0.967959i	$-0.580794\pi$
$829$	13.2911	−	7.67359i	0.461617	−	0.266515i	0.712724	+	0.701444i	$0.247461\pi$
$830$		0			0
$831$	−0.0289927	+	0.211034i	−0.00100575	+	0.00732068i
$832$	0.176460	+	2.01695i	0.00611766	+	0.0699251i
$833$	29.1693	+	13.6019i	1.01066	+	0.471277i
$834$	−19.8784	+	18.0103i	−0.688331	+	0.623647i
$835$		0			0
$836$			4.57055i			0.158076i
$837$	−4.66544	−	22.8654i	−0.161261	−	0.790343i
$838$	22.8981	−	22.8981i	0.791002	−	0.791002i
$839$	−2.05282	−	11.6421i	−0.0708712	−	0.401931i	−0.999520	−	0.0309713i	$-0.990140\pi$
$839$	−2.05282	−	11.6421i	−0.0708712	−	0.401931i	0.928649	−	0.370960i	$-0.120971\pi$
$840$		0			0
$841$	−44.4266	+	16.1700i	−1.53195	+	0.557585i
$842$	−26.8064	+	2.34525i	−0.923808	+	0.0808227i
$843$	−5.19964	−	41.2902i	−0.179085	−	1.42211i
$844$	0.0336436	−	0.0924350i	0.00115806	−	0.00318174i
$845$		0			0
$846$	−9.53301	−	37.2504i	−0.327752	−	1.28070i
$847$	−5.08850	+	1.36346i	−0.174843	+	0.0468490i
$848$	−3.05053	−	0.266887i	−0.104756	−	0.00916493i
$849$	−1.04911	−	27.5924i	−0.0360054	−	0.946970i
$850$		0			0
$851$	0.273436	+	0.0482142i	0.00937327	+	0.00165276i
$852$	3.45258	−	3.72550i	0.118283	−	0.127634i
$853$	2.93357	−	33.5308i	0.100443	−	1.14807i	−0.763956	−	0.645268i	$-0.776746\pi$
$853$	2.93357	−	33.5308i	0.100443	−	1.14807i	0.864400	−	0.502805i	$-0.167699\pi$
$854$	−3.22284	+	5.58211i	−0.110283	+	0.191016i
$855$		0			0
$856$	−14.3341	−	24.8274i	−0.489929	−	0.848583i
$857$	−33.6303	+	15.6821i	−1.14879	+	0.535689i	−0.901297	−	0.433201i	$-0.857384\pi$
$857$	−33.6303	+	15.6821i	−1.14879	+	0.535689i	−0.247491	+	0.968890i	$0.579606\pi$
$858$	−2.21736	+	0.279230i	−0.0756993	+	0.00953276i
$859$	18.6876	−	22.2710i	0.637613	−	0.759878i	−0.346378	−	0.938095i	$-0.612588\pi$
$859$	18.6876	−	22.2710i	0.637613	−	0.759878i	0.983991	+	0.178217i	$0.0570329\pi$
$860$		0			0
$861$	3.99262	−	12.4187i	0.136068	−	0.423230i
$862$	11.8627	−	16.9417i	0.404046	−	0.577038i
$863$	−9.57951	−	9.57951i	−0.326090	−	0.326090i	0.525007	−	0.851098i	$-0.324063\pi$
$863$	−9.57951	−	9.57951i	−0.326090	−	0.326090i	−0.851098	+	0.525007i	$0.824063\pi$
$864$	−0.495978	+	8.18489i	−0.0168735	+	0.278455i
$865$		0			0
$866$	48.0287	−	8.46876i	1.63208	−	0.287780i
$867$	62.0020	+	3.05688i	2.10570	+	0.103817i
$868$	0.855281	−	1.83416i	0.0290301	−	0.0622553i
$869$	−4.41177	−	3.70191i	−0.149659	−	0.125579i
$870$		0			0
$871$	−0.312045	−	0.113575i	−0.0105733	−	0.00384835i
$872$	1.16451	+	0.312030i	0.0394353	+	0.0105667i
$873$	11.7832	+	33.5446i	0.398801	+	1.13531i
$874$	−0.985869	−	0.569192i	−0.0333475	−	0.0192532i
$875$		0			0
$876$	1.56378	−	2.96315i	0.0528353	−	0.100115i
$877$	18.1337	−	12.6973i	0.612331	−	0.428759i	−0.225842	−	0.974164i	$-0.572513\pi$
$877$	18.1337	−	12.6973i	0.612331	−	0.428759i	0.838172	+	0.545405i	$0.183624\pi$
$878$	−13.9339	+	9.75663i	−0.470247	+	0.329270i
$879$	−4.86133	−	7.72641i	−0.163969	−	0.260605i
$880$		0			0
$881$	38.5171	+	22.2379i	1.29768	+	0.749213i	0.980002	−	0.198987i	$-0.0637651\pi$
$881$	38.5171	+	22.2379i	1.29768	+	0.749213i	0.317673	+	0.948200i	$0.397098\pi$
$882$	−12.7210	−	15.5116i	−0.428337	−	0.522304i
$883$	15.2412	+	4.08387i	0.512907	+	0.137433i	0.505984	−	0.862543i	$-0.331130\pi$
$883$	15.2412	+	4.08387i	0.512907	+	0.137433i	0.00692327	+	0.999976i	$0.497796\pi$
$884$	0.590280	+	0.214844i	0.0198533	+	0.00722599i
$885$		0			0
$886$	7.81768	+	6.55981i	0.262640	+	0.220381i
$887$	11.6632	−	25.0117i	0.391610	−	0.839811i	−0.607359	−	0.794427i	$-0.707771\pi$
$887$	11.6632	−	25.0117i	0.391610	−	0.839811i	0.998970	−	0.0453839i	$-0.0144511\pi$
$888$	−5.25850	+	8.15255i	−0.176464	+	0.273582i
$889$	21.2504	−	3.74702i	0.712715	−	0.125671i
$890$		0			0
$891$	24.9927	+	0.562915i	0.837287	+	0.0188584i
$892$	3.12148	+	3.12148i	0.104515	+	0.104515i
$893$	−28.5082	+	40.7139i	−0.953990	+	1.36244i
$894$	−3.09313	+	0.667484i	−0.103450	+	0.0223240i
$895$		0			0
$896$	13.5031	−	16.0924i	0.451108	−	0.537609i
$897$	0.0265943	−	0.0631956i	0.000887957	−	0.00211004i
$898$	15.6093	−	7.27874i	0.520890	−	0.242895i
$899$	19.6120	+	33.9690i	0.654098	+	1.13293i
$900$		0			0
$901$	2.48266	−	4.30010i	0.0827095	−	0.143257i
$902$	1.71688	−	19.6241i	0.0571660	−	0.653410i
$903$	13.3368	+	3.03558i	0.443822	+	0.101018i
$904$	1.22439	+	0.215893i	0.0407226	+	0.00718049i
$905$		0			0
$906$	−37.4057	−	19.7406i	−1.24272	−	0.655838i
$907$	3.71818	+	0.325298i	0.123460	+	0.0108014i	0.148718	−	0.988880i	$-0.452485\pi$
$907$	3.71818	+	0.325298i	0.123460	+	0.0108014i	−0.0252582	+	0.999681i	$0.508041\pi$
$908$	6.39013	−	1.71223i	0.212064	−	0.0568223i
$909$	−40.3316	+	3.07139i	−1.33771	+	0.101871i
$910$		0			0
$911$	−8.20345	+	22.5388i	−0.271792	+	0.746743i	0.726435	+	0.687235i	$0.241176\pi$
$911$	−8.20345	+	22.5388i	−0.271792	+	0.746743i	−0.998228	+	0.0595086i	$0.981047\pi$
$912$	36.2335	−	27.4802i	1.19981	−	0.909961i
$913$	36.4695	−	3.19067i	1.20697	−	0.105596i
$914$	−10.5269	+	3.83148i	−0.348199	+	0.126734i
$915$		0			0
$916$	−1.12953	−	6.40589i	−0.0373207	−	0.211656i
$917$	−7.01316	+	7.01316i	−0.231595	+	0.231595i
$918$	−50.1481	−	27.1916i	−1.65513	−	0.897456i
$919$			55.8452i			1.84216i	0.389370	+	0.921081i	$0.372693\pi$
$919$			55.8452i			1.84216i	−0.389370	+	0.921081i	$0.627307\pi$
$920$		0			0
$921$	−36.4951	−	11.7332i	−1.20255	−	0.386620i
$922$	57.0495	+	26.6026i	1.87882	+	0.876110i
$923$	−0.279807	−	3.19821i	−0.00920995	−	0.105270i
$924$	1.71249	+	1.32942i	0.0563367	+	0.0437348i
$925$		0			0
$926$	4.35356	−	2.51353i	0.143067	−	0.0825997i
$927$	−4.37471	−	7.77817i	−0.143684	−	0.255469i
$928$	−3.56716	−	13.3128i	−0.117098	−	0.437014i
$929$	43.9037	−	36.8395i	1.44043	−	1.20867i	0.501224	−	0.865317i	$-0.332883\pi$
$929$	43.9037	−	36.8395i	1.44043	−	1.20867i	0.939208	−	0.343349i	$-0.111561\pi$
$930$		0			0
$931$	−4.50286	+	25.5370i	−0.147575	+	0.836942i
$932$	3.48567	+	4.97805i	0.114177	+	0.163062i
$933$	−18.2805	−	16.9413i	−0.598478	−	0.554635i
$934$	−4.34306	−	5.17586i	−0.142109	−	0.169359i
$935$		0			0
$936$	1.67478	+	1.71293i	0.0547420	+	0.0559889i
$937$	14.6753	−	54.7688i	0.479420	−	1.78922i	−0.124551	−	0.992213i	$-0.539749\pi$
$937$	14.6753	−	54.7688i	0.479420	−	1.78922i	0.603971	−	0.797006i	$-0.293584\pi$
$938$	1.10524	+	2.37019i	0.0360873	+	0.0773895i
$939$	−22.5749	+	29.0798i	−0.736705	+	0.948982i
$940$		0			0
$941$	13.7044	+	37.6526i	0.446751	+	1.22744i	0.934973	+	0.354719i	$0.115423\pi$
$941$	13.7044	+	37.6526i	0.446751	+	1.22744i	−0.488222	+	0.872719i	$0.662354\pi$
$942$	−48.2799	+	24.7885i	−1.57304	+	0.807651i
$943$	0.495050	+	0.346638i	0.0161211	+	0.0112881i
$944$	43.4886			1.41543
$945$		0			0
$946$	20.6552			0.671557
$947$	−38.0843	−	26.6669i	−1.23757	−	0.866557i	−0.242941	−	0.970041i	$-0.578112\pi$
$947$	−38.0843	−	26.6669i	−1.23757	−	0.866557i	−0.994631	+	0.103484i	$0.967001\pi$
$948$	0.0496845	−	1.00774i	0.00161368	−	0.0327298i
$949$	−0.724290	−	1.98997i	−0.0235114	−	0.0645972i
$950$		0			0
$951$	39.4470	+	5.41939i	1.27916	+	0.175736i
$952$	12.7922	+	27.4331i	0.414599	+	0.889110i
$953$	−14.9234	+	55.6950i	−0.483417	+	1.80414i	0.103668	+	0.994612i	$0.466942\pi$
$953$	−14.9234	+	55.6950i	−0.483417	+	1.80414i	−0.587085	+	0.809526i	$0.699724\pi$
$954$	−2.55501	+	1.74650i	−0.0827214	+	0.0565449i
$955$		0			0
$956$	−2.56752	−	3.05985i	−0.0830396	−	0.0989627i
$957$	−40.1442	+	12.4094i	−1.29768	+	0.401139i
$958$	31.8330	+	45.4622i	1.02848	+	1.46882i
$959$	2.05655	−	11.6633i	0.0664095	−	0.376627i
$960$		0			0
$961$	−8.29622	+	6.96135i	−0.267620	+	0.224560i
$962$	−0.259378	−	0.968010i	−0.00836267	−	0.0312099i
$963$	−30.9992	−	11.6797i	−0.998936	−	0.376374i
$964$	2.02929	−	1.17161i	0.0653589	−	0.0377350i
$965$		0			0
$966$	−0.500021	+	0.203825i	−0.0160879	+	0.00655796i
$967$	−2.27121	−	25.9600i	−0.0730371	−	0.834818i	−0.941048	−	0.338273i	$-0.890157\pi$
$967$	−2.27121	−	25.9600i	−0.0730371	−	0.834818i	0.868011	−	0.496545i	$-0.165398\pi$
$968$	7.72854	+	3.60388i	0.248405	+	0.115833i
$969$	15.5544	+	72.0794i	0.499679	+	2.31552i
$970$		0			0
$971$			24.3222i			0.780536i	0.920701	+	0.390268i	$0.127618\pi$
$971$			24.3222i			0.780536i	−0.920701	+	0.390268i	$0.872382\pi$
$972$	2.56731	+	3.54828i	0.0823466	+	0.113811i
$973$	11.6294	−	11.6294i	0.372822	−	0.372822i
$974$	3.35887	+	19.0491i	0.107625	+	0.610372i
$975$		0			0
$976$	11.2096	−	4.07998i	0.358812	−	0.130597i
$977$	4.39652	−	0.384646i	0.140657	−	0.0123059i	−0.0166097	−	0.999862i	$-0.505287\pi$
$977$	4.39652	−	0.384646i	0.140657	−	0.0123059i	0.157267	+	0.987556i	$0.449732\pi$
$978$	−31.5208	−	13.2647i	−1.00792	−	0.424159i
$979$	−10.6057	+	29.1388i	−0.338958	+	0.931280i
$980$		0			0
$981$	1.26911	−	0.574487i	0.0405194	−	0.0183420i
$982$	−33.5090	+	8.97872i	−1.06932	+	0.286522i
$983$	−6.29396	−	0.550651i	−0.200746	−	0.0175630i	−0.0136609	−	0.999907i	$-0.504349\pi$
$983$	−6.29396	−	0.550651i	−0.200746	−	0.0175630i	−0.187085	+	0.982344i	$0.559904\pi$
$984$	−17.8727	+	11.2452i	−0.569760	+	0.358484i
$985$		0			0
$986$	94.4260	+	16.6499i	3.00714	+	0.530240i
$987$	6.96254	+	22.5237i	0.221620	+	0.716938i
$988$	−0.0441099	+	0.504179i	−0.00140332	+	0.0160401i
$989$	−0.316839	+	0.548781i	−0.0100749	+	0.0174502i
$990$		0			0
$991$	3.28793	+	5.69486i	0.104445	+	0.180903i	0.913511	−	0.406814i	$-0.133360\pi$
$991$	3.28793	+	5.69486i	0.104445	+	0.180903i	−0.809067	+	0.587717i	$0.800027\pi$
$992$	−6.42327	+	2.99522i	−0.203939	+	0.0950983i
$993$	−14.6059	−	19.2583i	−0.463505	−	0.611144i
$994$	−16.2520	+	19.3683i	−0.515481	+	0.614326i
$995$		0			0
$996$	4.30628	+	4.75293i	0.136450	+	0.150602i
$997$	−11.4987	+	16.4219i	−0.364168	+	0.520086i	−0.958864	−	0.283864i	$-0.908383\pi$
$997$	−11.4987	+	16.4219i	−0.364168	+	0.520086i	0.594696	+	0.803951i	$0.297272\pi$
$998$	9.88969	+	9.88969i	0.313053	+	0.313053i
$999$	1.27529	+	11.1373i	0.0403484	+	0.352367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.257.4		192
5.2	odd	4		135.2.q.a.68.13	yes	192
5.3	odd	4	inner	675.2.ba.b.68.4		192
5.4	even	2		135.2.q.a.122.13	yes	192
15.2	even	4		405.2.r.a.233.4		192
15.14	odd	2		405.2.r.a.152.4		192
27.2	odd	18	inner	675.2.ba.b.407.4		192
135.2	even	36		135.2.q.a.83.13	yes	192
135.29	odd	18		135.2.q.a.2.13	✓	192
135.52	odd	36		405.2.r.a.8.4		192
135.79	even	18		405.2.r.a.332.4		192
135.83	even	36	inner	675.2.ba.b.218.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.13	✓	192	135.29	odd	18
135.2.q.a.68.13	yes	192	5.2	odd	4
135.2.q.a.83.13	yes	192	135.2	even	36
135.2.q.a.122.13	yes	192	5.4	even	2
405.2.r.a.8.4		192	135.52	odd	36
405.2.r.a.152.4		192	15.14	odd	2
405.2.r.a.233.4		192	15.2	even	4
405.2.r.a.332.4		192	135.79	even	18
675.2.ba.b.68.4		192	5.3	odd	4	inner
675.2.ba.b.218.4		192	135.83	even	36	inner
675.2.ba.b.257.4		192	1.1	even	1	trivial
675.2.ba.b.407.4		192	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23715 - 0.866263i) q^{2} +(-1.45553 - 0.938839i) q^{3} +(0.0960923 + 0.264011i) q^{4} +(0.987435 + 2.42236i) q^{6} +(-0.677826 - 1.45360i) q^{7} +(-0.671958 + 2.50778i) q^{8} +(1.23716 + 2.73303i) q^{9} +(-1.78545 - 2.12782i) q^{11} +(0.107999 - 0.474493i) q^{12} +(-0.176418 - 0.251952i) q^{13} +(-0.420628 + 2.38550i) q^{14} +(3.43416 - 2.88160i) q^{16} +(1.88139 + 7.02145i) q^{17} +(0.836964 - 4.45287i) q^{18} +(-5.07203 + 2.92834i) q^{19} +(-0.378100 + 2.75214i) q^{21} +(0.365624 + 4.17910i) q^{22} +(-0.116642 - 0.0543910i) q^{23} +(3.33246 - 3.01930i) q^{24} +0.464527i q^{26} +(0.765143 - 5.13951i) q^{27} +(0.318634 - 0.318634i) q^{28} +(1.51659 + 8.60103i) q^{29} +(4.22026 - 1.53605i) q^{31} +(-1.57207 + 0.137538i) q^{32} +(0.601106 + 4.77337i) q^{33} +(3.75485 - 10.3164i) q^{34} +(-0.602668 + 0.589247i) q^{36} +(-2.08386 + 0.558369i) q^{37} +(8.81158 + 0.770913i) q^{38} +(0.0202409 + 0.532353i) q^{39} +(-4.62442 - 0.815410i) q^{41} +(2.85184 - 3.07728i) q^{42} +(0.429127 - 4.90494i) q^{43} +(0.390200 - 0.675847i) q^{44} +(0.0971868 + 0.168333i) q^{46} +(7.69135 - 3.58654i) q^{47} +(-7.70389 + 0.970146i) q^{48} +(2.84600 - 3.39173i) q^{49} +(3.85358 - 11.9863i) q^{51} +(0.0495656 - 0.0707870i) q^{52} +(-0.483003 - 0.483003i) q^{53} +(-5.39876 + 5.69554i) q^{54} +(4.10079 - 0.723079i) q^{56} +(10.1318 + 0.499526i) q^{57} +(5.57450 - 11.9546i) q^{58} +(7.43127 + 6.23558i) q^{59} +(2.50049 + 0.910105i) q^{61} +(-6.55173 - 1.75553i) q^{62} +(3.13415 - 3.65086i) q^{63} +(-5.70071 - 3.29131i) q^{64} +(3.39133 - 6.42609i) q^{66} +(0.884390 - 0.619257i) q^{67} +(-1.67295 + 1.17142i) q^{68} +(0.118712 + 0.188676i) q^{69} +(9.03942 + 5.21891i) q^{71} +(-7.68515 + 1.26605i) q^{72} +(6.65047 + 1.78199i) q^{73} +(3.06175 + 1.11439i) q^{74} +(-1.26050 - 1.05768i) q^{76} +(-1.88278 + 4.03763i) q^{77} +(0.436116 - 0.676135i) q^{78} +(2.04188 - 0.360038i) q^{79} +(-5.93887 + 6.76239i) q^{81} +(5.01475 + 5.01475i) q^{82} +(-7.55956 + 10.7962i) q^{83} +(-0.762929 + 0.164636i) q^{84} +(-4.77986 + 5.69642i) q^{86} +(5.86754 - 13.9429i) q^{87} +(6.53585 - 3.04772i) q^{88} +(-5.58181 - 9.66798i) q^{89} +(-0.246656 + 0.427222i) q^{91} +(0.00315146 - 0.0360214i) q^{92} +(-7.58484 - 1.72638i) q^{93} +(-12.6222 - 2.22564i) q^{94} +(2.41732 + 1.27573i) q^{96} +(11.8062 + 1.03291i) q^{97} +(-6.45906 + 1.73070i) q^{98} +(3.60649 - 7.51214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

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